Level 1 - Disintegrate
Level 2 - Incinerate
Level 3 - Disintegrate
Level 4 - Incinerate
Level 5 - Molten Shield
Level 6 - Summon : Tibbers
Level 7 - Disintegrate
Level 8 - Incinerate
Level 9 - Disintegrate
Level 10 - Incinerate
Level 11 - Summon : Tibbers
Level 12 - Incinerate
Level 13 - Molten Shield
Level 14 - Incinerate
Level 15 - Molten Shield
Level 16 - Summon : Tibbers
Level 17 - Molten Shield
Level 18 - Molten Shield
Exhaust - It slows down your target for 3 seconds so, this will help you a lot in gaining kills. But if your target has this spell too, i suggest you only use this during ganks or team fights.
Ghost - This spell can be used as an escape method or for chasing down targets for kills.
Heal - This spell is kinda useful during early game, but not until mid to late game starts. During mid to late game it may save you a couple of times, but i don't see it that much useful at that time.
Cleanse - This spell is pretty much a lifesaver when you are facing stunners or slowers. This might not be a bad choice.
Clarity - During early game Annie might have a mana problem if you don't use your Disintegrate spell properly, but mana problem is not that much a big deal during early game. If you don't want to use this spell then might as well buy a mana potion at the beginning of the game with Amplifying Tome.
Ignite - It deals damage depending on the enemy's level. This is kinda useful specially when your enemy (who has a very very very very low hp ) is trying to run. Cast this spell on that enemy and you won't bother chasing them anymore.
Flash - One of the best spells in League of Legends. This is somehow similar to Ghost spell. It is used for escape methods and for chasing enemies. In my case, i find this more useful than Ghost. I recommend this one for players who are level 12 +.
Revive - A very useless spell for me. Fighting enemies and getting yourself killed and returning quickly using this spell is a very stupid idea. Never ever use this spell.
Smite - Annie is not a jungler / farmer. No matter how much you want her to go jungle / farming, Annie is not for that type of gameplay.
Teleport - You may save a lot of time traveling in helping your teammates or saving a dying turret. Still, Annie is not that type of champion who can endure damage from 3 - 5 heroes just to save a turret.
Fortify - I really don't like this spell, even if it is kinda useful against turret divers. Might as well leave this to the support / tanks in your team.
Rally - Oh C'mon! I don't need to explain this one.
Clairvoryance - This is not useful enough to detect enemy heroes. You're lucky if you use this and happen to see enemies on the place you used your spell. This spell just goes by luck, seriously.