CBS has been releasing the Star Trek TV series on Blu-ray. To celebrate, and I suppose to entice you into buying them, they've posted snippets of the special features online. Ensign, chart a course for the Guffaw Nebula!
Season 2 Gag Reel
Michael Dorn (Worf) has trouble holding his scowl together, Jonathan Frakes (Riker) trips on a chair, Brent Spiner (Data) experiences a malfunction, and more. Note around the one-minute mark, you can see studio lights at the top of the bridge set.
Resistance is Futile
Worf versus his prosthetic teeth. My biggest laugh was at the end.
Season 3 Gag Reel
Here's a snippet of the Season 3 gag reel. Worf: "I never played with boys."
Season 5 Gag Reel
Here's a snippet from Season 5, via IGN.
Star Trek: Enterprise Gag Reel
Oh yeah, Enterprise is coming out on Blu-ray too.
There's more of this stuff on YouTube (there are 10+ minute gag reels for most seasons, and some have leaked online, though most isn't official). The best way to get this stuff is of course to buy the discs (TNG Season 1 is the place to start), with the downside being that they're super spendy. We also have a post with some more Trek bloopers, though the videos tend to be taken down frequently.