"B" - use in 3rd person to toggle zoom distance a bit (does exactly what mouse scrollwheel does, only instantly)
"K" - use when in 1st person in cockpit to center your view\
"K" - use when in 3rd person cockpit view (press F1 twice from 1st person view) - hold it down, move mouse to adjust camera freely! Great for screenshots
"Q" & "E" - use when in cockpit; appears to adjust yaw (thanks Animadversor)
"1" - while in Constellation chair, appears to deploy turret or crash the module
(thanks Lachrymose)
"~" - opens a console-like window that shows start up bugs/log (and also screenshot info, at least for two screenshots for me) (thanks Shadowlight)
"RMB" - click it to enable a HUD pop-up in the Hornet cockpit (thanks Stormy)
"TAB" - after using the ship customization "holotable", TAB will toggle the mouse cursor to select ships, drag 'n drop, etc. Might have to adjust camera a bit to see everything (a little to the left of center works for me) - (Thanks jimboking)
"Jstick" - "Joystick inputs work too btw, my Fighterstick controlled pitch/something" (thanks Silas Farseer)
"Once the turret is deployed in the connie it can be moved around with the mouse." (Thanks ProteusRift)
"1" - press 1 while seated in the Freelancer, it will move you to the second seat (Thanks BulletChief)