Can any bike crankset be exchanged for another?
The main intercompatibility issues with cranksets are the connection between the crank arms and the bottom bracket spindle.

Most bikes from that age (not to say all mountainbikes) use square taper bottom bracket, for which is very easy to find good quality cranksets.

These look like the leftmost spindle in the picture above (which also show newer types, that are less likely to be what you need):



You might also take a look at the page from where that image came, in the excelent website of Sheldon Brown:

http://sheldonbrown.com/bbsize.html

Other compatibility issues might be related to the length of the bottom bracket and the length for which the crankset was designed. Using different-sized bottom brackets and cranksets might result in a misaligned chainline, an ill-working front derailer, or in extreme cases a chainring running too close to the frame. This is so for tapered square, but I am not sure about the other types.