Can I recycle my broken plastic phone?

Of course you can! If you live in the UK try these websites:
http://www.recycle.co.uk/recycling-home-business/
http://www.tradeinmymobile.co.uk/consumer/index.asp

If you don't live in the UK - sorry! Can't help you there I'm afraid.

If you're in the US:

Check out stopwaste.org -- or this direct link: http://stopwaste.org/home/index.asp?page=36&actionview;=Go2&actionstep;=2&Go2DropDown;=ele&Mat;=CELL

(Alameda County specific, but most of the programs listed are national)

The Sierra Club runs a cell-phone recycling program in partnership with Staples. You can take your phone to any Staples store and drop it off for free. They will refurbish your phone and distribute it in the developing world to people who don't have phones. If it can't be refurbished they will take care of the recycling.
You can find out more at http://www.sierraclub.org/cellphones

there are a lot of place for dated cell to go to. First, you can sell it to second-hand store, to refurbish or re-sell, Second you can give to the poor people who realy want a cell,
otherwise they are hardly not erased if only by bury in landfill, burning will produce more noxious gas and energy wasting.
see cell recycle.

There is one place again for the UK, that actually lists all of the places that will pay you for your phone, and compares the amount that they will pay you. It lists loads of places to recycle mobile phones across the UK