Our source in the Bay Area (who took these WWDC pre-conference photos), has informed us that Apple's release date for OS X Mountain Lion is Thursday, July 19, 2012.
During at the WWDC 2012 Apple reminded us that they have been on a one year major iOS release schedule since 2007's first iPhone. This seems to be the plan also with OS X. No more 2-3 year wait between OS releases. Instead Apple intends to stick to an annual update cycle which continues to make Microsoft's OS release schedules looks slow if not pointless. July 19th's release date would be 364 days since OS X Lion's release (July 20, 2011).
Apple choosing July for their OS X release is a great play. WWDC will be a month old, and no new Apple announcements are likely until mid-September after school starts back up again. It will be a launch with nothing around it, pushing more interest back to the Mac. Microsoft can attempt to take some headlines with their tablet launch, but Apple looks to be able to control the headlines for quite some time.