Microsoft has announced what kind of hardware you will need for Windows Vista.  The good news -- you won't need much to run it in its most basic mode.  The bad news is that the full Vista goodness will require a very high end system and lots of memory.

CPU wise, only 800Mhz is needed.  Realistically, you should have a 2+ Ghz machine to get the most out of it.  In theory, only 512MB of memory is needed to run Windows Vista, realistically you should have 2 GB of system memory.  It's on the GPU that you will need to have a really beefy setup.  To get the Vista "glass" effects you need a video card with at least 128MB of video memory.

For the official specs, see the linked to CNET article.