There were quite a few scenes on the various Star Trek shows where music was “performed” by the crews of the various ships. I haven’t found them all but this selection of videos captures a fair few good scenes.
This first clip has Uhura singing “Spock’s Song” from the episode “Charlie X” (probably the only worthwhile moment in the whole episode). It will certainly feed the fires of Spock-Uhura subtext conspiracy theorists who feel the connection was there long before J.J. Abrams rebooted the franchise.
A lot of people seemed to detest William Riker’s trombone. I’m not sure why. Nonetheless, this scene is one of the best holodeck sequences from Star Trek: The Next Generation because it’s so relaxed and uncompromising. Most of the holodeck scenes focused on the fact that it was fake but in this episode (where binary-something aliens take over the Enterprise) Riker has been drawn into the most realistic holodeck experience of them all.
This clip is taken from the so-called Hippy episode (“The Way To Eden” — which just about everyone but me detested, but hey, I only liked it for the music). Brother Adam celebrates the impending death — er, arrival of his little group of dreamers (led by the insane Sevrin) on the planet they think is the true Eden. This brief song has been called “Yeah, Brother”.
Here is another clip of Adam singing “Gonna Live, Not Die”. I always thought he sounded a bit like David Clayton Thomas from Blood, Sweat, and Tears. Not everyone agreed with me. This song is the least DCT-like performance, but there is still something of that BS&T feel to it.
This next clip is not like those from the original series. Taken from Star Trek: The Next Generation, it treats us once again to a teary-eyed Vulcan (this time Sarek, as he approaches the end of his life and career).
And finally, this clip is part of a series of videos that have been uploaded to YouTube. There are several scenes in this one, including Brent Spiner singing (as Lore). I could have done without the Klingon birthday bash, but oh well.