Not Updated For Current Season
My first build, and what I usually use when I'm playing Annie or any other AP-based caster. The Archangel's Staff at the end is entirely optional; I normally play without it.
If you want to have a bit of fun, you can actually take this Annie build to the jungle around level 7 or so. I've gone in at lower levels, but it doesn't really pay off for the rest of the team if you decide to do so, as you'll fall behind in EXP.
When buying items for this particular build, I start out with basic boots, and then upgrade them to Sorc. Shoes. The Rod of Ages should be built by first buying Sapphire Crystal then Ruby Crystal and upgrading to Catalyst the Protector. Your Blasting Wand should be bought shortly after, and then finally the RoA. If you end up making enough gold before your second recall, however, feel free to skip the building steps and buy the completed item. I only build as I do not recall unless absolutely necessary, and since I don't ever invest in mana or health potions, getting small items is much more beneficial to me than just waiting around for the gold.
Mejai's Soulstealer is actually another optional item; sometimes I forgo this and get an Abyssal Scepter if I feel I would be better off against the opposing team with it.
Rylai's Crystal Scepter should be built just as the Rod of Ages was (I go Giant's Belt, Blasting Wand, and THEN Ancient Tome), unless you earn the gold to buy it outright, of course. The reason I do the Giant's Belt first, even though it is the most expensive, is because Annie is fairly squishy champion and the additional HP comes in very handy. After you've gotten your Sorcerer's Shoes, Rod of Ages, Mejai's Soulstealer, and Rylai's Crystal Scepter (or maybe just the Shoes, RoA, and Rylai's), you should look into obtaining Zhonya's Ring. After that, I sometimes go for either a Manamune or Archangel's Staff. To mix things up, a Hextech Gunblade can be fun, too. :)
If you're going to solo lane, health or mana potions may be of interest to you in the early stages of the game; you can buy these with leftover gold from your first purchase of boots. You can also buy health and/or mana potions when you are laning with someone else, but I usually don't go for potions of any kind with this build.
As far as runes go, you should have:
9 Glyphs of Force (ability power per level)
9 Seals of Evasion (dodge)
9 Marks of Insight (magic penetration)
3 Quintessences of Potency (ability power)
I'm currently experimenting with switching my Seals of Evasion out for Seals of Alacrity (atk. speed), but I'm not too sure about them yet.