Odyn's helps a lot, since it gives a lot of MR and 10% magic resistance lowering. The big thing is that you need to space yourself so you don't get smashed into a wall. Sometimes it's unavoidable, but a lot of the time it's not.
As for Poppy counterpicks, anyone with a reliable stun can shave off a lot of her DI time if she does DI on that character. Likewise, slows can eliminate her movespeed buff to some degree and give her less ability to space a proper wallslam. Nothing can perfectly counter her during DI, unfortunately -- unless she DIs you. Obviously if you're the DI target, you should spam CC on her and make yourself a big problem. This is more attractive if you're an attractive target.
Magic damage is pretty effective against Poppy, just because her W doesn't give any bonuses to it and Rylai's has a nice slow. Anivia in particular I like against Poppy; she's a good "soft target" that can be made a lot harder to kill with items, she has slows and a stun, although her base movespeed is poor. She also doesn't do a lot of her damage in single big hits, with the exception of her chilled E combo, which lets her deal with Poppy's passive a bit.
I personally don't think there's a really good "counter" to Poppy, but she's still manageable with good play. Don't get caught out of position too often and you shave off a lot of her effectiveness. Poppy is best when she has good teammates who can put you in a bad spot or let Poppy get into a good one.