Sonic Generations

Q: Does this game have multiplayer mode

No this game does not have a multiplayer mode, although I wish it would, like sonic adventure 2 battle

Q: Is this a game for people who just want alot of running in a Sonic game or is there alot of stopping and story and destroying bots?

Mostly running. Not nearly as much stopping as some of the other recent (bad)games. All in all they pretty much got it right here and it pretty much runs smoothly the entire game. Not much story (nothing like sonic adventure) and not so many annoying enemies. A great game!