512 MB RAM, is a good start.
Jimmy

As much as you can afford.

JJK

As inexpensive as memory is now I would use as much as your computer can support and you can afford.

if you're tight for money, unles you will be doing a lot of work with pictures, between 256 & 512 should be ok. I did about 6 sports highlight videos & 12 interviews (all several minutes in length) on a P3-667 & 256mb DDR. :)

You can run multiple instances of vegas at the same time. That's very helpful and needs more memory.

You can "render to RAM" complex segments which allows you to preview footage from composites and footage with a lot of effects on it. This is very helpful and the more memory you have, the more helpful it is.

I tend to run a lot of programs simultaneously, so I think the minimum amount of RAM on my main system starts at 512MB. A healthy Vegas system probably starts at 1gig. I use 1.25 gig and have run up to 4 of instances of Vegas. Some folks here who do a lot of RAM renders have 4 gig and Vegas will soak that up during a RAM render when doing a final render, it's mostly CPU power at that point and a small bit is disk speed. New technologies like HDV will probably want more memory too.

If it was not my main machine, I could go for 256MB, but I'd still want more. Happy Friar's right too, you can go with a minimum memory and then if Vegas makes you some money, you can upgrade later.

I've run over 12 instances of Vegas, rendering in most of them and editing in the rest, with only 256MB of RAM. No problems. There didn't even appear to be much paging to speak of.