Annie is one of my most played champion, and if you want, i can point out all her weaknesses so that you can abuse her.
-Whenever she goes in for a Q (with or without stun), harass her back, early her damage is rather low. There's a delay before the spell hits you that gives you ample time to fight back.
-She has no mobility and short range (for a mage) She's very vulnerable to ganks.
-She's really bad when there are no front lines in her team, so if her support jungler and toplane are squishy, she'll be useless in teamfights and be forced to waste her cooldowns on your initiator.
-Any amount of MR is enough to deny her, Banshee's Veil just outrights denies her. Tanky and AD champions have multiple items to counter her burst and CC.
-Unless she's fed, she can't one-shot you even with her whole combo. When mid/lategame comes and she has more AP, you too should have built some defensive items by then to counter. If you are still squishy and have no MR, there's noone to blame but yourself.
-She's really easy to bully if you outrange or can keep her away.
-If you can push the minion wave into her turret, you'll force her to use her spells on minions, exposing her to free harass. Her waveclear is relatively bad early, compared to a lot of midlaners.
That's all i could think of right now, i'm sure i missed of few points, but that should be a decent starting point.
Having played Annie a lot i can say that her biggest strenght is her roaming potential. Strap Mobility Boots on her and help side lanes with a guaranteed stun. Obviously she does have some easier matchups.