First off, I'd attempt to load it up at your place to start wiping sensitive information off it, such as stored credit card details or Word documents.
If the computer can still be used, a charity shop may be interested. Phone around a few of them and explain what you have for them. Bear in mind they may not be able to understand what the model numbers are or anything, so try not to bamboozle them too much. Ask them if they will clean the computer's hard disk too.
If no-one wants to know, but the system works, use the Belarc Advisor (on most PC Advisor cover discs or found online through Google) to note down the bits inside it, and maybe offer it on eBay. If you are technically minded, you may wish to put individual parts on eBay instead. Remember to go to the Post Office to find out what the maximum postage and packing would be.
If it is unusable or unsold, then you may wish to chat to your local Recycling Centre. They can offer advice for old computer units, and might say "bring it down here and we'll get rid of it for you".