Anything, for decent GUI performance, 64mb or more RAM, for a GUI/desktop environment like GNOME or KDE, make that 128mb,preferably 256mb or more.
Your looking at console only memory overhead with a new kernel of about 38mb, maybe less, depends on kernel choice and how much hardware youve got installed, linux can run on 4mb easily with minimum services and hardware.
64mb is enough to run a "live" CD distro, 128mb-256mb works better, dont need more than that though really.
CPU---> assuming no games, 500mhz w/100mhz fsb will allow playing video smoothly
700mhz will allow direct playing of dvd smoothly
1ghz will allow recording a video signal into mpeg on the fly @640x480 w/o dropping frames
If you want an eye candy intensive GUI, 1ghz or better realistically with 256mb ram
after that, your into the bonus or overkill zone
disk space needed, average distro, 800mb to 1Gb, but, thats with prettymuch every piece of software you will need with many duplicates, with everything available for linux software wise in the most complete distro's, your looking at almost 3Gb's of disk space used
with some planning and some work you can setup a very capable system with any socket A or p3 CPU and probably never need an upgrade
with a little more work and planning, you dont need anything special at all to surf the net and do office type stuff, an 8yr old p100 system will work just fine
hints:stay away from bleeding edge brand new hardware, overclocking is not needed, mass huge amounts of ram arent needed either,beware of ATI graphics cards, pick printers carefully(very carefully--postscript is good), stay the hell away from "dumb" hardware--->winmodems are bad news, so is anything else thats all software to run,linux likes intelligent hardware
Linux is completely modular, you can pick and choose what you want to put in it, eye candy means ram and cpu cycles just like any OS, but linux has lots of choices of everythng, it runs on anything from a pda to a mainframe built by IBM, and there's apps to fit prettymuch any need in that range.
If youve got some extra parts laying around, check the HCL listing at linuxquestions.org to make sure its ok(comaptible), or just ask me in the linux forum and I will check, and throw a system together, ive already dealt with many of the problems linux can throw at you at one time or another.
I highly recommend doing a little research first, http://www.linux.org
are good places to start, so is http://www.lowfatlinux.com
, it isnt windows, there is a learning curve, starting cold turkey isnt easy for many people.