I have an old PII computer sitting around that is doing absolutely nothing but taking up space. I had thought about trying to use the case for a rebuild but I think even that is out of date. What can I do with it? How can I dispose of it properly?

Yank the hard drive out of it and then give it to anyone that wants it(or pay someone five bucks to take it)

Shoot it.

Quoted: Shoot it.

To many upgrades to make it viable, make it into a security monitor along with a day and night cameras

Put Damn Small Linux on it.

Reformat the hard drive and install Linux.  

Folding.

You can try Linux on it (or ask around if anyone wants to try Linux). It's a LOT easier to try Linux as a full install on a separate PC than it is to try a "live distro", as that way you can get online with your regular Windows/Mac PC and look for help when you can't get the Linux one to work right.
And most older hardware has Linux-compatible drivers, so problems are minimized.
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Nobody will pay for such a PC anymore.
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If you just want to toss it (or can't find it a new home) then find a wiping program and run that on it first, to get rid of the data on the hard drive (as well as easily possible). "Eraser" is the name of one that includes a feature to make a "Nuke Disk" that you boot off of to wipe a PC's hard drive.

Eraser is just a nice wiping program to have anyway--but the Nuke Disk is available alone from other places as well.
~

Quoted: Folding.

+1
ARFCOM folding team

You play old games?

Quoted: Quoted: Folding. +1 ARFCOM folding team

Is this like SETI@home but aimed towards biological research?    

Wipe the disk and donate it to a school, church or Boys\Girls Club. Most not-for-profits are always looking for hardware and can never afford it.

Quoted: You play old games?

X-Com.

Folding is a good use for older machines. 500mhz or thereabouts is the lower useful limit nowadays, IMHO.

Quoted: Quoted: Quoted: Folding. +1 ARFCOM folding team Is this like SETI@home but aimed towards biological research?

Yes. See here folding.stanford.edu/  A little more practical, and more likely to benefit you or a loved one at some point.

Quoted: Quoted: Folding. +1 ARFCOM folding team

+2

i've been running it for several months now

There is also The Lad Vampire.  You can help shut down fake bank websites setup by scammers by wasting their bandwidth as well.