First of all, welcome to my build ! This is my first guide so please no raging. Anyways, I spent a lot of experimenting with this build, and this is the best I've come up with so far.
This guide is not all-out pure AP. Instead, a combonation of AP , HP and MP.


Pros

Awesome Nuke.
You'll want to adopt her when you get your teddy bear.
Laning Domination
Best Skins (IMO, I play with Reverse Annie)

Cons

Easily ganked early game
Nothing else to it really.

You'll want to start off with a [*] Sapphire Crystal and 2 [*] Health Potions. You want to do this because you will be harrassed quite often early game. You can start off with a [*] Doran's Ring, but you will have not as much laning sustainability compared to the Sapphire Crystal and Health Pots. After that, you will want to get a [*] Boots of Speed for increased moving speed, (mostly for ganks and positioning.) Next, you will want to rush a [*] Rod Of Ages, buying [*] Catalyst the Protector first. This is mainly because of the squishy-ness of Annie early game/mid game. I consider the HP and MP bonus quite important to Annie. Then, you'll want to buy a [*] Giant's Belt. Now at this point, you will be almost unkillable when 1 v 1. Unless you are ganked, laning at this point will be a breeze. Now, the game will be coming to an end, either you lost your 2nd line of towers or you have taken out the enemies 2nd line of towers. You will want to get a [*] Rylai's Crystal Scepter. This is the main item to your victory. The HP, and AP will both contribute to your massive nuking skills. If the game continues, buy an [*] Rabadon's Death Cap. Once you get this, your nukes will take out so much HP that you won't even think that you have that capability. For some reason, the game still continues buy an [*] Void Staff , the AP and Magic Pen is the most useful item since you already have your core items.

You'll want to get your (Q) Disintigrate first since it is your main farming skill. Last hitting minions with your Q will give you the edge because of its massive damage and mana regen. Your (W) Incinerate, will be another skill, this skill , along with your teddy bear Tibbers, will be the skill that makes the enemy retreat in fear. Your (E) Molten Shield, may not seem that important, trust me, it is. Get this at level 4, you will actually have a chance to survive ganks and teamfights (since you will be focused alot). Now, your weapon of mass destruction, a cute little teddy bear. "Ohhh ! It's so cute! It looks so fluffy, am I right?" "WRONG!", This may seem like a harmless doll, press your R, and left click, your enemies will face a slow, painful death of AoE damage and massive claws swiping at their face.

Farming for Annie is quite self explanatory. For those who have a hard time farming, or to those who don't know how to play Annie, which is highly unlikely...

Four simple steps

1. Auto attack a few times.
2. Get the minion to about 1/4 Hp
3. Press your Q button, left click
4. Gold, Free mana back!