The purpose of this build is to maximize the damage and stuns Annie can put out which means also having lasting power to do that. I believe Annie to be one of the top casters (personally I only see anivia/fiddle/kass as real threats to that) and when played right, will always be contributing to a team regardless of a bad start.
Summoner Skill Reasoning: I chose ghost because of the ability to either survive/kite an enemy from a constant safe distance/mobility in a chase or gank. Kiting (spamming spells while avoiding being hit by an enemy(ies) you) is extremely vital on any spammable caster as a 300 hp Annie can drop a 1000 hp Yi by just firing off spells by running to lower the amount of hits Yi can get in. This tactic is absolutely vital for anyone who is serious about Annie or else she will die often.
Flash should be fairly obvious as I currently believe it to be the best summoner skill as the offensive and defensive nature of this skill is unrivaled. No amount of items or runes can replicate instant ganks with tibbers or escapes/gain distance to kite more.
I personally believe ignite is currently still too specialized as single target dps should be left with your physical dps allies. Similarly with exhaust, I don't think Annie has any problem stalling heroes with her stun and the -25 MR here would often be minimized in effect because this build uses magic penetration extensively.
Skill Choice Reasoning: First off, I vastly prefer to play a dual lane with Annie, because most good players mid will either farm/play cautious and simply not die without a gank. Having Annie in a side lane allows either A) the 2nd hero to farm safely while Annie makes a parameter to stop enemies or B) Provides 2-3 extra nukes to a champion already with a couple nukes of their own which is easy lane control/first blood. First level is easy as incinerate allows Annie to charge her stun up from the spawn and is able to use it for any level 1 activities your team may try. The reason for maxing incinerate first is due to the point about facing multiple heroes in the lane and usually when Tibbers is down, I'll be using this to initiate a stun on the enemy. I don't get Molten Shield early as I think Annie is better off with higher damage rather than a stun as Disintegrate on a really short cooldown and hopefully Annie doesn't need the armor/MR to resist this early on. Also it has a high cooldown limiting it's effect on charging the next stun.
Mastery Reasoning: I prefer to either have the 9 on offense to go towards AP/.66% crit with 4 in sorcery and 1 in the 15% pen or just dump the 9 in defense if I feel my team is going to have a hard time disabling the enemy. The 21 in utility is fairly straightforward, ignore the 5% extra mana boost, 30% longer monster buff (don't believe it works yet) and basically fill up the rest excluding the summoner spell specific ones that don't apply to ghost/flash.
Rune Reasoning: I'm not sure if the game takes decimals but this assumes it doesn't. So the magic pen runes are there for a nice rounding of 10 magic pen (hence the one in glyphs) while the 1 armor pen rune is mostly for me not getting annoyed by having reduced damage against creep spawns early game. The cooldown rounds to a nice ~4% at level 18 (thanks to the seal cd rune). While I attempt to patch any mana problems I have with a couple clarities in seals. Also I believe the MR/Armor runes to be fairly important as each point basically increases your health against magic/physical by 1%. And as it stands, it is almost always superior in durability than say 19+ hp the scaling runes give. As for the problem with early game health, I have 2 quints of HP which currently are 6 times stronger than their non quint counterpart considering most quints are only 2-3 times more powerful, this is huge. Also consider 60 hp on a hero like annie who starts with around 420 hp. 60 Hp is effectively boosting Annie's base HP by ~15%.
Item Build: The separated pieces are mostly there for reference in when to get each piece. I like starting with the mana booster as it allows gold for health potions, but if a team is truly focused on level 1 ganking/dragon (nerfed this patch however), I could be persuaded to get the health booster. I usually attempt to get enough gold for catalyst and boots before I leave the lane but if I happen to either die and don't have enough for catalyst, I'll get boots. I often aim for a 15 minute rod of ages (with boots and maybe a vision ward if needed) while stacking magic pen and -cd% after. Often after getting grasp, I'll either get banshee or rylai's depending on the situation but usually I just get potions of fortitude and brilliance while warding as usually the game is winnable from here.
The reasoning behind these exact items is to focus on magic pen and cd% reduction to achieve maximum damage and stuns. As we already know, each point of magic resist gives effectively 1%+ health against magic damage. So 50 points would reduce enemy spells by 25% and 100 would reduce enemy spells by 50% and so on. Because of the the low AP ratios(0.6-0.7) on Annie, it is far more effective to stack magic penetration. While sometimes I go void staff if my enemies are truly stacking magic resist, most enemies will tend to stay around the 60 mark until late game but by then it's mostly about stunning for your carries rather than DPS as they'll do far more damage than any caster. Grasp gives an extra boost in almost everything Annie needs and even provides a extra target nuke in case one target may live through a combo. The rod of ages is obviously for durability/some extra damage as Annie is already usually the dominant hero early and maintains it for most of the time the rod is powering up.
I hope I've covered all the bases but I believe this is one of the best builds possible for Annie. Though feel free to add any suggestions(with reasoning) or questions about the build.