Eric...hardcore- sure. But I LIKE it! I guess I'll do something like that when I finally build my dream stand. Just not sure how succeptable it is to scrapes etc.
Jason- if cheap is your real goal, then using either a cheap shower curtain or some of the clear vinyl (like drip cloths in the paint section) I suggest not going with the thinnest they have though, if you're planning to put a sump or something else in there.
There's the hardcore sealing method that Eric posted which is the other end of the spectrum. However, if you're really just worried about the bottom of the stand a drip tray like Phong posted should work fine. Something like that probably can't be bought commercially though, so TAP plastics or some other local plastic store is your best bet for a non-DIY method. Give them the dims you want, and also mention that it needs to be water proof. If they won't guarantee that, then you can just buy a tube of weldon 16 (or borrow some) to run along the inside of the seam.