Early game
In early game with annie you have to start farming with your spells so you can have the stun for your next magic attack then you can keep it in a emergency because annie has low health or you can use it to stun the opponent if you are sure that you can take kill and escape or just to take kill if you are in the mid lane.Also you can use DISINTEGRATE if you want to stun surly or you can try to stun with MOLTEN SHIELD if you want to escape from 2 or more enemy champ you can stun all of them together.

Mid game
In mid game Annie is kindda powerful to kill one champion in only 5 seconds with her stun if she use it with Tibbers and then se can cast Incinerate and then Incinerate but she can die easily so keep an eye on her when you are fighting.

Late game
In Late game Annie can kill anemies easily but you have to be with the rest of your team because if you are going to well in this game like with score 30/4/* they will sure try to kill you and you can die easily if they stun you or if they slow you

Pros
Aoe stunning
Tibbers too strong (good)
Molten Shield it's good against ad
Incinerate gang stunning
Disintegrate sure stun

Cons

Difficult to be played against ad like (Xin,Master yi,Kong maw and more champ)
Annie has low life so she can be killed very easy

Annie is very good farmer because of her two spells Incinerate that can kill more than 4 creeps together and Disintegrate so she can kill 1 to 1 creeps.

: This is a great escape method, or gank method for Annie. It'll help you get a lot more kills, and save you a lot more from deaths. Must have in my opinion.

: This is to add to your insane DPS, and help get those kills that should have been. Trust me, the more DPS on Annie, the better. :)

Of course, not everyone is going to be like me, and I can't expect everyone to love the way that I play, so here are some other spells that aren't too bad to have on her:

: Again, this can be used as an escape method or to chase down some kills that you need to get, I personally think you're better off with Flash but some people prefer Ghost.

: Since I've been playing Annie basically since I've started League, I don't find this as useful as someone who is new to her would. It may save your *** a couple times, it may be a waste, I'm not going to rule it completely useless, because heals, are well heals.

: This again, will help you keep enemies close for kills, let's you get off more spells and such. But to be complete honest, I'll be damned if another team member doesn't already have this, but again, it has it's uses.

: Early game, you may run into mana trouble with Annie if you mess up your Disintegrate kill shots, or you've been harassed or whatever the problem may be. I'm not going to lie though, once you the Sapphire Crystal on your way to your Rod of Ages mana won't be a big problem. But again, it isn't completely useless.

: This can have it uses in team fights, and can certainly be the difference between life or death in some cases. Personally, I wouldn't choose it over Flash or Ignite but if you know you're going up against some stunners or slowers in a custom, might not be a bad choice.

These next spells, you should never, under any occasion what-so ever get. Ever. Really. I mean it.

: Losing out on Flash, or Ignite, just so you can come back and die again because you didn't have Flash, or Ignite, just is stupid.

: But Dyruus, you could come and help your teammates or save a turret anywhere! While this is true, and while you may get kills this way. Believe me when I say, if Annie is the one teleporting to save a turret against 3-5 other people. You won't live.

: You can't jungle, as much as I would love too with Annie, you can't. Just don't grab it, don't think I need to explain myself here.

: I just don't like this ability in general, but especially for Annie. You should always have your stun close to, if not up to stop turret divers. Best leave this for the support/tanks.

: Do I really need to explain this?

: It's not that it isn't useful, but, it isn't useful enough to replace what you could grab instead.