Annie is a champion that scales well, so what I could offer are the following:
PREVENT FARM
As soon as Annie gets rod of ages, she'll be very very powerful already. If you let her farm, you're looking at a pre-6 rod of ages. Push her under her tower and poke/aa when you can. Annie will still be a nuissance, but less so. She may be able to farm under turret, but not without costing a lot of mana. Plus, this prevents her from roaming as well, so keeping her in check is good.
POKE HEAVILY
Annie has low mobility. Champs that can stun or poke from a nice distance will be safe from Annie's stun, and will win trades. Some recommended players are Brand, Lux, Morgana, Veigar (requires a bit more skill with his stun), orianna, galio, xerath, ziggs, leblanc, or syndra. They are not skill shot oriented and can do some nice poke from large ranges. I always play brand or orianna, simply because you can escape when you see the flash stun coming in with the slow.
DRAIN HER MANA
She is useless without it. Drain her mana by forcing trades, poking her, pushing the lane, and forcing her to farm from a distance. When she has no mana, start to manage yours a little more to have an upper hand in ganks.
PUNISH HER STUN
She will stun level 6 with immense burst. She will try it. Guaranteed. Especially if you've taken damage. What i do if I'm lower than her is I let her push a bit, watch her movement, and mimic it near my tower. if she dives i punish it by bursting. Most likely she'll get a kill, but if you used everything possible you can take her down with you, maybe even first.
NOT RECOMMENDED CHAMPS
It's often assumed that Ahri is great because she can sort of stun and has high mobility. However, her strongest burst comes from charm and all other spell tactics. The downside is in fact that Ahri's abilities work best with no minion waves, and her charm actually allows annie to come closer to you. Do Not Play Ahri Vs Annie. Some other champs I'd steer away from are Akali, Katarina, Leblanc if you're not good with her, and Fizz, as she can punish Akali Katarina and Leblancs desperation with their ultimates and actually render them useless and also destroy them when they get near. Fizz Kata and Akali are melee champs or require close contact, and annie punishes them so much more for them than other champs. Some people play it well, but I'd also veer away from yasuo. Annie has the upper hand unless she is slower and has worse reaction times than you, because she can punish your E movement and after your ulti to burst incredibly hard. Zed is also a risky play, but also provides a safe option.
Hopefully this provides some insight. Basically the pointer I'll end this with is watch her carefully. If she has a swirly thing, she has stun, expect aggro.