I'm fairly new to Annie, but I've been having lots of success with the way I play and build her. this build is for early and mid game DOMINATION. But don't be fooled, you are a force to be reckoned with late game as well.
I will take a little bit of time to stress how important CS is. YOU NEED FUGGIN MONEY. This is what separates average players from noobs, honestly learning how to get KBs WILL change your game. Every mini kill you don't get is wasted gold for your team. So please, just get your KBs down.

Simple runes, early game spell pen Greater Mark of Magic Penetration and AP from quins Greater Quintessence of Ability Power and yellows Greater Seal of Ability Power, late game AP and spell pen from reds Greater Mark of Magic Penetration and blues Greater Glyph of Scaling Ability Power, along with your build it makes you shred people with your combo.

I've checked a couple other guides and they have you use MP5 yellow runes Greater Seal of Scaling Mana Regeneration, I have no objection to this and in some situations I would encourage it. The only reason I don't use it is because I'm cheap, and I don't usually have mana problems after my Rod of Ages.

Pros
-stupid damage
-great situational CC and possible initiate
-you feel like a boss
-easy to play
Cons
-squishy
-easily focused down
-CC can really screw you over (play smart)

Laning with Annie can be a bit challenging because of her limited range. yes, her damage is pretty impressive but her range is wimpy. Kassadin, Cassiopeia, Morgana, Gragas, Galio, and many other champions out range Annie pretty well. this can be a challenge. The way that i counter this, with all the other champions i play as well, is move awkwardly. Maybe fake pressure, run towards them and back off after they try and predict your next step. Predictability will make you lose often, I know this because this is how I beat a lot of players. This is what I'm saying when I say Play Smart.

This is where Annie dominates, this is where I play possibly the most aggressive. With my rune setup and a Doran's Ring I'm sitting around 37 AP at lvl 1. At level 1 I don't poke at all unless they make a point of it and run into all my minis to hit me once, I'll chuck back a Disintegrate if they do. By level 2 I have hit all the minions with a Disintegrate and gotten all the CS, now I have my Incinerate, this is when I start to win my lane, get your stun up, by last hitting minions with your Disintegrate. Press your opponent really hard, even if he has boots, try and lane them. Or, if they left you, show them your damage with a Disintegrate Incinerate combo, at lvl 2 I've killed people with 2 combos and an Ignite, stupid amounts of damage. Besides being really aggressive GET YOUR FUGGIN CS...... Riot made it SOO easy to farm with annie... Disintegrate everything, practice try not to miss a minion for 5 waves.

Think of levels 1-5 as being a setup for a kill, as soon as u get your ultimate you should have a kill in your pocket. Everything you do early game is a set up for your kill at level 6, once youre 6 look for the opportunity (could even be a gank on a different lane) , Summon: Tibbers Disintegrate, Incinerate, Ignite. They should be dead after just that, but use your auto attacks if necessary.
PS - you can use Disintegrate first to make sure you get your stun off, but opening with Summon: Tibbers makes for most damage, because of your bear's arua.

As of this point if you are keeping up with your CS you should atleast have your Doran's Ring, Sorcerer's Shoes, and Rod of Ages. Its damage time baby!! A single full combo can kill usually any squishy, and usually get anyone else down to retreating health. You can roam if you want try and pick up some kills, because at this point you have enough health to survive a counter gank. (if you try and gank and they focus you) Basically you can be more aggressive mid game because of your scary damage, and your balanced items, masteries, and runes.

Your health isn't so impressive anymore so now you must be extra careful, but your damage is. My only piece of advice for Late game is do not be out of position. Continue to farm, and guess what!!! Its become even easier!! At the third rank of your Incinerate spell and with a minimum of 150 AP you can one shot all the caster minions.

- good escape for such a squishy caster, just an amazing spell, I use it on pretty much every champion I play.
- I can't tell you how many times I've gotten kills because of ignite, amazing spell to have.

I don't see how many other spells could be that useful with Annie in general and not just this build for her. Exhaust is a great spell, but I feel that having Ignite is a much better combo for Annie. Clarity is just bad in my opinion, with every caster I play I don't have continual mana problems that can't be solved with items.

Offensive Last Items

- Great item, great health, great AP. Definatly a viable option for your last item space, but I don't feel the need for it. The slow is not worth it to me when I usually kill someone in a single combo.

- This is the item I usually fill the last item space with, great situational, nice armor and another huge stack on your AP. If you're someone who doesn't use your items I wouldn't recommend this, because the use is half the item, so it won't be used to its full potential if you buy it for the AP and the armor

- always a great item if you think you can handle it ;)

Defensive Last Items

- I personally have never tried this, but I can see the potential if a Yi wont leave you alone, Molten Shield + Thornmail and he'll probably kill himself before you get to stun him.

- I can see this being used, if you've got a LeBlanc or some other caster that is more annoying than you. I personally haven't had to use it, but i can defiantly see the situation where it would be necessary.

- Great MR and great AP, plus more spell pen. Please and thank you. Use it if you've got any kinda of consistent AP damage on the other team Singed, Rumble, Alistar, even Madred's.

PS - unfortunately if you are being raped by AD carrys there are only really 2 Options as far as what I believe to be viable options for armor, Zhonya's Hourglass and Thornmail.

Team play with Annie is tricky, shes so squishy that you can't just run out there blow all your CDs then try and run away, cause you'll get focused by Nocturne, Warwick, anyone that can touch you. So then how do you effectively use all of your spells without getting killed? What I do is keep myself visible to the team. (meaning I don't try and flank them with the bushes) and wait for my tank to slow someone down and or CC them. Even if it is a bruiser he wont have nearly as much MR than a tank. So ill usually start to move in for the stun, depending on who else is near by. (if a Warwick or Nocturne were near by I would probably wait to use my burst. (yes im scared of their ultis) After my burst they're probably dead, boom 4v5. Now they are either going for one of your squishies or going after you, if they are going after you kite them with your spells and your partner's slows and just wait for your cooldowns, which should be very short because of Morello's Evil Tome. If your team continues to push, follow with them use your spells on whoever you can to try and get your stacks back up, once you've got another stun (but no bear I recommend using Incinerate if you are positive youll stun more then 1 person) use it on a squishy, preferably. Rinse, wash, repeat.

Think I'm ******ed for the way I build Annie? Well then tell me. I would like feedback, any suggestions or arguments. I plan on making more builds for the other champions that I believe I play well, let me know if you think that's an awful idea or if its a great idea.