Will any 700c tyre fit my rims?

maxppp Posts: 39
edited October 2009 in Road beginners
My front tyre is a 23 and my back is a 28 or poss a 32, was wanting to put some slightly more 'rugged' 700c tyres on. Ive see specialized do some 700x38's which almost look like mountain bike tyres.

Are these larger width tyres designed to fit any 700c rim or am i more restricted than i'd hoped?