Annie, like Veigar, has no mobility - but Veigar's ult is an anti-AP nuke and he can theoretically have as much AP as he wants. Ryze's ult gives him movement speed and he's inherently tankier and tends to build tankier items.
The trouble with Annie is not a lack of counterplay - it's a lack of knowledge about how to counterplay her. She's incredibly vulnerable when she's at 0-1* stacks on her passive (*unless she's got her ult up and you give her the time to get all 4 abilities off), and a good Annie will disregard her passive while farming. This is to your advantage. Annie has a relatively low spell range compared to champions like Ahri, Lux, and Veigar.
The reason people don't like playing against Annie is because she's pretty much an anti-bullshit champion. If you come at her with a bullshit all-in champion like Fizz or Zed, you're gonna have a bad time. The best way to counter an Annie is to poke her down from afar and keep a reasonable distance. Lux, who has received some pretty nice buffs in the past few patches, is a really good counterpick assuming you're able to stay away.
Alternatively, playing a tankier champion against Annie wouldn't be a bad idea either. Ryze, Cho'Gath, etc. might be viable picks against Annie.