MendUK.org database has been going for a while but seems to have been re-publicised recently with the launch on 12 January 2005 of a new National Mobile Phone Register Immobilise.com. UPDATE: that MendUK link just links to Immobilise now but the crossed out registration link below still works; however the main service now seems to be Immobilise.
It was set up because details of lost or stolen property were only available to the local police force - there was no co-ordinated centralised database that police could search to track down owners outside their local area.
It's worth registering your phones, PDAs, laptops, MP3 players etc, basically all your valuable mobile gear. It's free. I'd recommend registering through MendUK rather than Immobilise as the former offers a secure connection (through an abundance of caution I always prefer using secure sites where possible); also, MendUK is more obviously geared up for gear other than phones, if you'll forgive the pun. Don't forget to click the link for a secure connection first, or go direct to the secure registration page here.
Apart from your name, address and contact details you'll need the serial number of your device (IMEI number in the case of a mobile), make and model. You can also edit the register to add descriptive info e.g. the colour of the device, any custom covers etc.
If your mobile phone is lost or stolen, there's just one number to call to block it whatever your network (08701 123 123 - this number can be used even if you haven't registered details previously) call your network to get the phone blocked, and you should also report the loss or theft online at Immobilise (though the MendUK link still seems to work). It's probably a good idea to report it to the police anyway as you'll probably need the crime reference number to claim on your insurance policy, and certainly it's best to report it if you were mugged.
Tip: to display your long IMEI number on most phones, just enter *#06# on your keypad, or check the label under the battery. (It's always sensible to note down in a safe place your IMEI number and also SIM card and PIN numbers as soon as you get a new phone, anyway).
For fun: enter your IMEI number here to find out all sorts of things about your phone much of which you probably already knew - and analyse your phone number, SIM number etc if you wish. Should that sort of thing amuses you...
If you register, you might have a chance of getting back lost phones and other gear if a kind passerby finds it and hands it in. For stolen mobiles etc, you're probably stuffed even if the networks blacklists the IMEI - there's lots of ways for thieves to change IMEI numbers with software (though that's illegal, but if they're already a criminal they're not going to care are they?). (Not the same as unlocking a phone's SIM, see e.g. UnlockMe).