Microsoft has released its requirements for running Windows 7.
www.microsoft.com/windows/windows-7/get/...em-requirements.aspx
If you read their page, the big thing to key up on is the memory as many older XP machines usually only came with 256MB or 512MB of memory. I wouldn't wory about the processor speed if your machine is running XP as most machines now and then have at least a 1GHz or faster CPU.
Durring my process of helping people in the KMC area, I was given a laptop that someone wanted Windows 7 on. Luckily I had an additional 256MB of memory laying around that I stuck in the Laptop for free (I'm a very nice guy). So now the laptop is up to 512MB, and I installed Windows 7 on it. Everything seems to be working great. I actually think the PC runs faster than it did with Windows XP. I know this, because I installed a fresh copy of XP SP3 before I installed Windows 7. Now the true test will be how the customer likes it. Oh ya, If you don't believe me then just check out the screen shots below.

UPDATE: It looks like updating this old PC to Windows 7 isn't going so good now. The problem is the integrated graphics card, and the drivers that were written for it. As you can see I have Windows 7 running on the PC, but the resolution is only 800 X 600 as Windows is using a generic driver. The video card is an Intel 82852/82855 GM/GME chipset so I will try the latest driver from the Intel site to see if I can get it to work. The Intel sites states that it only supports up to Windows XP, but that may be because the graphics card is no longer supported. I'll update if this works.