Out of the many hotel booking websites, which has the best cancellation policies or which do you recommend?
There seems to be large deposits required on some which are non-refundable.

It depends... that can vary site to site. Some rates you choose have no cancellation penalty. Rates that are pre-paid typically have the largest cancellation penalty. I use asia-hotels.com. Generally, if you cancel in advance (24 to 48 hours, typically) there is no charge. But always read the fine print.

Check out directrooms.com.

I used http://www.planetholiday.com/ last year for Vietnam. They didn't charge us until 10 days before our stay. Here is the cancellation policy.

CANCELLATIONS: If you wish to cancel your booking after you have received
a confirmation, a cancellation fee of US$10 will apply. Any cancellations
received LESS THAN 5 DAYS before arrival (including requests made within
this period) are subject to a 1 (ONE) night cancellation fee, unless you
are notified otherwise in the confirmation email. The additional US$10
cancellation fee will NOT be charged in this case. Failure to arrive at
your hotel will be treated as a late cancellation and will incur a
cancellation fee as indicated above.

I just came back from a trip where I used sawadee.com. Not sure what the cancellation policy is, but they were very helpful and all four of our bookings went off without a hitch.

Leslie