It seems Intel is still changing the site but you can navigate to a compatibility chart for your specific system. Other information is more difficult to find.
DQ965 mobo supports the following:
Intel Core 2 Quad w/1066 Mhz bus
Intel Core 2 Duo w/1066 or 800 bus Intel Pentium D w/800 or 533 bus
Pentium 4 w/800 or 533 bus
Celeron D w/533 bus
The page for the mq is http://www.intel.com/support/motherboards/desktop/dg965mq/sb/CS-026612.htm. Differences can always exist for different version boards so you should always check. Some of these processors are most likely no longer available, expecially for older boards. This can be reached through Support > Support > Discontinued boards.