Rammers have always been a problem in this game. It's one of the reasons I gave up on it all. That, and the fact that the PC version is pretty damn glitchy.
There are some non-contact races though - off the top of my head, Rally is non-contact, and same with Trailblazer. There are probably more than that as well. I'm pretty sure it's sorted into the contact and non-contact types when you go into the Multiplayer section, but most people just go with all types.