DO NOT let them take control of your computer, but please try and get as much info as you can.
If you are in the UK:
Tell a consumer programme about it:
http://www.bbc.co.uk/watchdog/gotastory/
http://www.bbc.co.uk/radio4/youandyours/liz_barclay_consumer_series.shtml
or perhaps your local or national paper. Oddly, in the April the BBC said there “wasn’t any interest” in this story. Take a moment to prove there is!
Also, report it to: https://secure.consumerdirect.gov.uk/reportascam.aspx
There are also threads on http://forums.moneysavingexpert.com/showthread.html?t=1613667 and
http://www.hotukdeals.com/item/502631/call-from-microsoft-maintenance-dep
The Register have an article about it:
http://www.theregister.co.uk/2009/04/10/supportonclick_scareware_scam/
Note: The Staffordshire Police have also issued a warning about this:
http://www.staffordshire.gov.uk/NR/rdonlyres/3ECA6489-52AC-4A64-A48E-4E44743CB9CB/90090/TelephoneComputerSupportWarning.pdf