Hey guys
This is my first attempt at a build/guide so I hope its ok. I'm not fully aware of all the numbers involved behind this build so don't expect anything like "and that means you'll be doing 3.4x more damage" this is just a build that works for me 90% of the time (the other 10% is when you get put in a team with people who..... well they need more practice) and i hope it can work for you as well.

The most important part of this build is the Spell Vamp which I haven't seen in most of the Annie builds out there. While I don't claim to have the only build that's viable I do know that Spell Vamp has changed Annie from a Nuker into an almost tanky survivor that will come out at the end of a team fight still asking for more!

Pros:

Insane damage
Provides your team with stun capability
Can rise to an almost offtank status
Fun to play

Cons:

Can be terrible without timing and practice
Squishy early game

On top of having one of the longest ranges for auto attacking in the game which can be abused on melee champions early game Annie also has some deadly spells:

Pyromania: (Innate): After every 5 spell casts, Annie's next offensive spell will stun its target for 1.75 seconds.
This is what makes Annie such a good nuker, not only will they not be able retaliate but they also get to hold still while you unleash your fury. This skill is better used in conjunction with Summon: Tibbers for the AOE stun in a team fight but you don't have to waste Tibbers just because you want to stop someone getting away, Pyromania used with Disintegrate can follow someone out of the normal range and lets your allies catch up to secure a kill. Knowing how to read your situation and time Pyromania correctly will separate a good Annie player from a great one; this may take practice but will be well worth it.

Disintegrate: (Active): Annie shoots a mana infused fireball, dealing magic damage to her target. The mana cost is refunded if it kills the target.
Cool down: 4 seconds
Range: 625
Cost: 60 / 70 / 80 / 90 / 100 mana
Magic Damage: 85 / 125 / 165 / 205 / 245 (+0.7 per ability power)
You want to use this skill as a build up for Pyromania this means you can get farmed a little, still have full mana and get your stun up all in one go. You will have to time your skill properly to last hit but later in the game you will usually kill a minion with one hit form this skill. This spell is like a heat seeking missile, if it manages to go off it will always hit, skills like Ezreal's Arcane Shift and Kassadin's Riftwalk just delay the inevitable, many times I have killed or stunned them as they disappear over a wall because the fireball locked on just as they "escaped". As this spell has the lowest cool down of all your abilities it should be used first if Tibbers is unavailable or second if he is, after the stun (if used) has worn off there is only a few moments before you will be able to use it again.

Incinerate: (Active): Annie casts a cone of fire in front of her, dealing magic damage to all enemies in the area.
Cool down: 8 seconds.
Range: 625
Cone Width: ~45º
Cost: 80 / 95 / 110 / 125 / 140 mana
Magic Damage: 80 / 130 / 180 / 230 / 280 (+0.75 per ability power)
This can be used as a lesser Summon: Tibbers as it can stun anyone in the cone but is more used as damage output. This spell is second to Tibbers in damage but available more readily, combined with spell vamp this can regenerate huge amounts of health in one hit and can turn the tide of any battle, try and hit as many things as possible and you should be fine.

Molten Shield: (Active): Places a shield around Annie for 15 seconds that increases her armour and magic resistance. Additionally, enemies will be dealt magic damage whenever they use auto attacks on her while the shield is active.
Cost: 25 mana
Cool down: 30 seconds
Armour & Magic Resistance: 10 / 20 / 30 / 40 / 50
Magic Damage: 20 / 30 / 40 / 50 / 60 (+0.2 per ability power)
This puts Annie in a league that most nukers cannot achieve and this is what makes her off tank (almost) combined with Abyssal Mask your defences will rise up to a point which most nukers could only achieve by crippling their damage output. This spell adds up to the Pyromania count but will not activate it so activating Molten Shield just before a team fight wont put you out if the stun was already up. It is best to use this ability if you can see there’s going to be a conflict with other players but there are times when it can effectively be used to eliminate minion waves.

Summon: Tibbers: (Active): Annie releases her bear Tibbers from his toy prison, dealing magic damage to enemy units in the summon area. For a limited time of 45 seconds, Tibbers can move and attack at Annie's will, while continually dealing magic damage to surrounding enemies.
Cool down: 120 seconds.
Range to center of Summon's AOE: 600 (estimate)
Radius of Summon's AOE: 150
Radius of Tibbers' Aura AOE: 200
Continual Magic Damage: 35 (+0.2 per ability power)
Cost: 125 / 175 / 225 mana
Summon Magic Damage: 200 / 325 / 450 (+0.7 per ability power)
Tibbers:Attack Damage: 80 / 105 / 130
Health: 1200 / 1600 / 2000
Armour: 30 / 50 / 70
Magic Resist: 25 / 45 / 65
Annie's most well known spell and the one she is most feared for. In Combination with Pyromania results in an AOE stun which lets your team gain the upper hand and almost defiantly win the fight. Annie's main goal in a team fight is to make this happen, and do as much damage as possible at the same time. While Tibbers does not have to be used with Pyromania he can in some situations be used last when everyone is low on health for guaranteed kills. Because Tibbers is an AOE the range of the spell is actually longer than just the initial range, keep this in mind when someone is trying to make a run for it. As I will mention later Summon: Tibbers when used with spell vamp can dramatically increase your health regeneration, one of the reasons for making the build. Overall Tibbers should try and be saved for 2 or more people if you are with an ally or just to overwhelm someone in a 1vs1.

This will be quite brief:
The sequence chosen ensures that you aren't maxing out one of your main sources of damage without neglecting another as I have seen on some builds.
Taking Disintegrate first I usually last hit minions to slowly build up my stun, some use Incinerate first at home so that stun is ready for first attack, them come and cast one spell and run, this seems pointless and I avoid it.

I use this build all the time, none of the items are situational and I personally wouldn't change a thing. It's all in order of purchase so here goes...

I start with Doran's Ring because:
1. the mana regen combines with your runes and masteries and you can stay in a lane longer.
2. There’s no point having Magic Penetration without anything to penetrate with, 15 isn't much but combined with its other bonuses it's a great starting item.
3. that health you get makes you just that little bit harder to kill early game

Next get Sorcerer's Shoes:
Combined with your already high Magic Pen you are now doing true damage to most champs and you only have a Doran's Ring, plus you now have increased movement speed

Rod of Ages:
This item is very important and that’s why it's the first major one. My item sequence above recommends what you buy a Blasting Wand first, this makes you allot more dangerous and I always get this before a Catalyst the Protector. But if you are feeling harassed then I recommend buying a Ruby Crystal and working your way up to Catalyst the Protector before the Blasting Wand.
The health and mana that Rod of Ages provides are the most important in this item, I see the extra Ability Power as almost a bonus (but not that bigger deal that I would just get a Banshee's Veil instead) Now you are a real threat out there, by now some champions will be getting their Magic Resist up a bit, but with this item up and running your (nearly) 40 Magic Pen just got more to penetrate with and so it wont effect game play too much.

Rabadon's Deathcap:
Now come the big guns, and from now on any more Magic that you get/have has an influence on that 30% increase. Now as tempting as it may be DO NOT buy a Blasting Wand first, save and get a Needlessly Large Rod, this ensures you are doing as much damage as possible.

Will of the Ancients:
Here is where the magic happens... Firstly you need to build the Hextech Revolver, just saying. Now with this item you become very hard to kill, because of your masteries Disintegrate cools down quickly, with Incinerate close behind. Because of this you are able to keep up a briefly delayed onslaught which heals you for the massive amount of damage you are doing. But that just goes without saying really (DUH!! Spell Vamp heals you idiot!!) But while Tibbers is running around scorching everyone, you are getting healed passively, it almost doubles your health regeneration rate, this combined with your Molten Shield enables you to ride you some of the storm of a team fight. Annie can survive those few moments and cast her Q and W again, healing back any damage they took anyway. So often I have done a typical Annie; do massive damage then try and see if I can survive those few seconds before I can cast again. Since experimenting with spell vamp I have found the results to be amazing. Even if you don't like this build try spell vamp all you Annie players!

Abyssal Mask:
By now you will notice that Annie has reasonably high defences (with Molten Shield activated) but is lacking in the Magic Resist area (MR) this item solves this problem but also adds a few bonuses. On top of increasing your MR you decrease enemy MR, this adds up to that magic pen you already have which in turn means you heal yourself for even more when you cast those spells (which have 70 more ability power behind them). With these items you should find you can almost take the role of an offtank (almost) either way you are extremely hard to take down or tank and your kill to death ratio will be impressive.

Void Staff:
At this point you sell your DR if you haven’t already once you have room for another Blasting Wand. You will already be doing allot of damage to enemies and squishy players will take one look at you and use all available summoner spells to try and get away, but this last item means that not even tanks that stack up magic resist can handle your fury. With their further decreased magic resist you will nuke for more damage and therefore heal for more. This combined with that extra ability power makes you all but impossible to kill.

For masteries I take a typical caster 9/0/21 mastering flash Haste and ghost Blink of an Eye . This improves cooldowns and mana regen, it also increases ability power while increasing the usefulness of your selected summoner spells.

The runes I have chosen mean a slightly weaker early game, but ensure that later on even tanks will think twice before they "handle" your damage.

Firstly all those Magic Penetration runes add up to just under the same value as a pair of Sorcerer's Shoes, which means when you actually get a hold of those shoes most of the champions that you face (especially that early in game) will have no resistance and you will do true damage!!

The mana regen per level seals were added into the rune page after finding Annie lacking slightly when it came to mana regen. But these runes combined with the chosen masteries, Doran's Ring and Disintegrate's passive will mean you will only have to leave the lane to buy.

Now I know that not everyone will agree on my summoner spells but these are the ones I'm comfortable with. I don't go for Ignite just because when your nuking nothing survives to be ignited. These spells ensure Annie is mobile and can get into and away from battles quickly if necessary.

Flash:
This spell can result in a " Kassadin Riftwalk" effect as you flash over walls then nuke your enemies, I use this spell as my "offensive" spell, although it can be handy if Ghost is down to Flash over a wall to get away.

Ghost:
I use as more of a "I'm over my head" spell for a quick getaway, but occasionally Flash might be down and you need to just get that little bit closer....

MIDDLE LANE:
Ok I personally prefer not to be mid, I always offer it up to anyone who I know is capable of it just because there are generally more opportunities to gank the more enemies there are. However you will often get asked to take mid and you need to be prepared. If you get asked to leash you should certainly help out as there may be opportunity for an early gank, but be aware that you are quite squishy this early into the game and you should wait till enemies are distracted until you join the fight.

Once you start laning be aware of who you are facing, this will determine your play style for your early game.
If the enemy team has decided they want to put a melee champion mid which can happen be sure to abuse your huge range and auto attack when ever possible, staying just out of range and slowly taking their health down. If you end up with Mordekaiser make sure are moving around allot because that Siphon of Destruction has a long range and maybe just try to stay behind your minions and use your long auto attack range to farm until you level up.
Generally though you will be facing another ranged champion, the only ones you have to worry about are the ones who can out-range you like Brand who's Pillar of Flame requires you to constantly move around and stay further back than usual and Caitlyn with Piltover Peacemaker which has a similar effect. Apart from a level 6 Kassadin you shouldn't have too much trouble with your laning opponent.
Regardless of who I am facing I try to play like this: Last hit minions with Disintegrate to build up your Pyromania until you are level 2. Once you have your second spell you can start putting some pressure on the enemy, especially squishy ones (my favourites are Teemo and Ashe although you shouldn’t follow her too far unless you are confident of victory). Just use Disintegrate and once they are stunned follow up with Incinerate then back off, this will make most people use up one of their potions (if any). Now just keep using Disintegrate whenever they get too close and build up your stun again on them or minions. Pretty much repeat this until you are level 6 and you get Summon: Tibbers.
At this point they may be at home healing, if they are go to top or bottom lane (usually the one where the enemy has extended beyond halfway) use ghost if you feel you could miss the opportunity or not get back in time. Once you get there initiate with Tibbers and Pyromania (flash if you need to) this gives your allies a chance to move in on the stunned opponents. Your allies should help you out and secure you at least 1 kill/assist if not more.

If your laning opponent has decided they can stay in lane then let them push a little, this gives you more space to run after them if they manage to survive your first attack. Once they are over halfway you can wait till they are closer or until they have used up a certain spell either way when you are ready pop Molten Shield and make sure your stun is up then Flash to them (they are usually out of range otherwise) and drop Tibbers on them followed by Disintegrate then Incinerate. When the stun wears off they will have very few seconds to react and cast Flash or Ghost before you can cast Disintegrate again, if this does not kill them they will be very low on health and will want to go home... press the advantage and to some damage to their tower. If you didn't kill them don't worry you will get them next time and you have shown them what you are capable of, they will be wary of you, which is psychological warfare.

This process should be continued, keeping in mind to call MIA if they leave the lane, and even following if you know where they went (possible kill). You should always be looking for opportunities to get kills weather it’s an overextended top or bottom or your opponent is low enough make sure to not over extend or you can end up with a weak early game.

TOP OR BOTTOM LANE:
Here the process is the same but opportunities for kills are more frequent and easier to get with an ally at your side.
Right at the start of the game I try and leave home ASAP to get to the bush closest to their tower, just so you have advanced warning of when an enemy is coming, although most people will say I'm crazy for doing this I would say I get to the bush before my enemy 95% of the time. Once the minions get close start doing what you usually would as for middle lane.
You can use the bush as an extended "element of surprise" with your Flash especially if your enemy is unaware of you being there.

TEAM FIGHTS:
Your job in team fights is to dive on anyone squishy like poor Twisted Fate and eliminate them quickly. I would recommend waiting briefly in team fights until the enemy team has bunched up before dropping Tibbers and aiming the rest of your spells at your target squishy, this ensures you will firstly get more assists and kills but also makes less trouble for your allies finishing the enemy off. Try not to be the centre of attention either, try to stay on the outskirts of a fight while cooling down to maximise you usefulness as your auto attacks won't do much. Your Molten Shield is there to help protect you if someone manages to get through everything and come for you, you will only be vulnerable briefly as your abilities cool down then you can punish them for attempting such foolishness.