Step 1: Before you crack it open...
Thanks to MrJentis for some more ideas.
Before you go ripping it open remember that you can reuse the whole computer and not just some of the components.
Linux is an open source OS that you can install on your old computer and use it as a everyday computer, for those of you out there that are not geeks that just basically means its a OS like windows XP that people give away free that you can use. You could do endless things with linux and there is a distribution to suit every computer.
This is for some of the better spec computers out there. Its is the most like proper a OS and it is the most user friendly. It can easily do everyday tasks like Surfing and sending email's. I needs:
1 GHz x86 processor
1 Gb of system memory (RAM)
15 GB of hard-drive space
Graphics card and monitor capable of 1024 by 768
Either a Cd/Dvd-drive or a Usb socket (or both)
Internet access is helpful
Ubuntu's system requirements have escalated over the last few released but there is a alternative version based on Ubuntu called Xbuntu
500Mhz x86 Processor (At the very least!)
256 MiB of system memory (RAM)
2 GB of disk space
Graphics card and monitor capable of 800x600 resolution
This is a slightly less user friendly version of linux. Is is for those less functional PC's with not as good a spec. It needs:
CPU : Pentium 166MMX
RAM : 64MB
CDROM : 20x and up
Damn Small Linux
OK if none of the above options have worked for you, you must really have a scrappy computer. It is very basic and is not user friendly. It requires
486dx or 100% compatible processor
16mb ram (24mb recommended)
dual-speed CDROM (quad-speed or better recommended) (thats 2x or 4x)
1.44mb floppy drive (for boot floppy, if needed)
There are loads more distrabutions try http://www.linux.org/
Now I have never done the following options before so I can't go into detail on how to do them but you can google them:
Turn it into a server (web, printer, file etc.)
Put a big hard driver in it and make it a jukebox
Put a TV tuner into it and a big hard drive and make it a PVR
Use it as a firewall
Use it as a stress reliever
Automate Your Home
Use it as a answering machine
Make the monitor into a aquarium
Make it into a rendering farm
Trade It in
Put it in your car
Give it away/Donate
There are some more in the comments!