If you disable virtual memory all that happens is your system will run out of memory for processes quicker. (The same thing happens if you leave VM enabled but run out of disk space for swap files) Processes that request memory won't get it, and may or may not do something sensible as a result.

Since running out of memory tends to be an unusual occurrence, many programs don't deal with it at all well, and may behave erratically or just plain die. Even programs that do deal with it properly may die, since that may be the only sane thing to do in an out-of-memory situation.

This will cause you problems if, for example, one of the system processes (like the window manager) needs more memory and can't get it--you may well find your login session dies.

I really wouldn't do this unless you actually need to test what happens when the system runs out of memory (like if you're stress-testing an application you're writing)