From the soundtrack to Head (Bob Rafelson, 1968), here's the Pre-Fab Four, i.e. The Monkees, with a version of Mike Nesmith's very cool "Circle Sky."
Recorded absolutely live, with the guys playing all the instruments.
Obviously, The Monkees were not one of the great live bands, but for at least the duration of this song, they were clearly capable of delivering some convincing garage rock goods. In any case, I bring the whole thing up because the Criterion Collection has just released a fantastic new restored version of the film in question -- in widescreen and with a stunning new 5:1 Surround soundtrack, with the music remixed directly from the original 8-track masters. Suffice it to say that this is the first home video version of Head to do it justice; deliberately Fellini-esque and screamingly funny career suicides don't come any better. Plus, Carole King's "Porpoise Song," the movie's theme music, is the single best Monkees track ever.
I should add that the new Head comes in a box set -- DVD or Blu-ray -- featuring similarly restored versions of (among others) Easy Rider (in stereo! woohoo!), The Last Picture Show and Five Easy Pieces, all seminal works from that now vanished Golden Age of risk-taking American commercial cinema. The whole thing will set you back about 70 bucks over at Amazon, which is pretty reasonable, actually; if you haven't asked for an Xmas present from someone you love yet, I'd go for it.