Somewhere on you rim,there should be a sticker that gives the rim's width(it'll prolly say something like 622 x NN). Here's a chart that tells you what size tires will fit on what rims:
http://www.schwalbetires.com/tech_in...dimensions#rim

Frame and fork clearance will also be a factor. Unless you're in actual mud/sand/snow,width will be more important than tread;a 37mm slick will work better than a 32mm cross knobby. What bike are you riding?