Um, I'm not sure if he meant to be, but I think Dynamic was asking if you can swap different-sized tires, not wheels. I've never tried doing this, but--and someone can confirm or correct this--I'm pretty sure that it won't work. You have to match the tire BSD (i.e. the 'size', 27" or 700c) to the wheel: if you have a 700c wheel, you have to put on a 700c tire, same with a 27" wheel and tire (they have to match). I've recently inquired as to whether the width of the tires have to match the width of the wheel, and the general response I got was that it does not: as long as you have the right BSD size, then the tire will fit. (But note if they're 27" tires with smooth sides, no hooks on the rims, then you have to also deal with that. There's a thread in the past week about this question.

Converting wheel sizes, on the other hand, while a far more involved endeavor, can be done according to the guidelines given by previous posters. Main issue is brake reach (you also have to confirm hub spacing, but that usually isn't a problem).