This is my first build to put up here. If you were looking for a highly in-depth guide, I'm not your guy. I don't like to over explain something that can be easily tested. Anywho, I chose Annie as my favorite champion because I think she rules. Not much else to say there.

Magic Penetration is always good, Health is underrated on Annie in my opinion, and Ability Power never killed anyone. Unless they were the target.
See what I mean about not overexplaining?

Archmage's Savvy- Yay AP!
Deadliness- The other two are for Summoner Spells I'm not using.
Sorcery- Yay CDR!
Archaic Knowledge- Yay Magic Penetration!
Burning Embers- Extra AP for using Ignite is fun.
Good Hands- I'm impatient. Not that you should be dying.
Perseverence- Nice to have, even though it doesn't make a massive difference.
Haste- Get away or catch up faster ^_^
Awareness- Leveling up fast is a good thing.
Meditation- More mana regen.
Quickness- Again, nice for catching up and running away.
Intelligence- More CDR. Less time to drop your pedobear again.

Ability Tome- I personally hate Doran's items when a little luck will save you just as easy. Plus the extra damage on your Q this early is really nice.
Sorcerer's Boots- Magic Pen, what more can you ask for?
Rylai's Crystal Scepter- The health and slow are awesome, especially this early.
Will of the Ancients- Spell Vamp saves my life too often to ignore.
Rabadon's Deathcap- Pretty much core for every caster out there.
Void Staff- More Magic Pen, yay!
Lich Bane- The addition of Annie's AP to her autoattack is killer.

Now, depending on the situation, instead of LB, I'll get Mejai early, Or Zhonya's Hourglass or even Abyssal Scepter later. Get what keeps you alive best.

Really, your E isn't required early. I put it at level 5 because I'd rather not get caught in a situation where I wish I had it. The rest is just a general guideline I follow.

Ghost- Get away/Catch up
Ignite- Inflict more pain.

Why not something else? I don't feel like using them. Exhaust and Clarity can be good though.

Pros:
Pedobear
Nuke
Playing a six year old
She's amusing
Stun

Cons:
Kinda squishy if you aren't careful
Isn't incredibly easy to play