Take how ever much computer RAM you currently have to run what you run now, double it and increase your CPU performance by about 25% to accomplish the same thing on Vista is a decent guideline.
At a minimum, Vista will need 1GB of RAM to reasonably run any basic applications. 2GB minimum if you want to play any DX games. 4GB if you want the same game performance a 1GB XP system delivers.
And if you want to run Aero (the new Vista desktop), you will need a hardware accelerated 3D video card with 256MB of RAM, as a minimum to get the same performance from the desktop as XP delivers now.
Those are general guidelines, but should be pretty close to reality.