The clip of B.J. Thomas performing on The Ed Sullivan Show that I posted here the other day was obviously a lip-sync job. I don't think anyone watching that show over the age of ten was supposed to think B.J. was actually singing. I get the sense that such performances were prevalent during the heyday of the variety show, and of course the technique was revived in the glory days of MTV.
The alternative to lip-synced TV performances would seem to be a full live run-through of the song, a la The Midnight Special or Saturday Night Live if you're not Ashlee Simpson. But there's a choice between these two that seems to have fallen by the wayside, wherein a band sings live vocals to the original backing tracks. The Beatles may have invented this (although all that means is that the earliest example I can find is of the Beatles): For the famous televised performance of "All You Need Is Love," in 1967, the boys performed to a prerecorded backing rhythm track, with drums, piano and background vocals. (Unhappy with his vocals, John Lennon overdubbed the verses for the single release.) I'm sure there was probably a heyday for this sort of thing, maybe on Soul Train? I don't really know.
But it's the best choice, isn't it? Most groups just try to re-create their music onstage with as much fidelity as possible anyway, with the exception maybe of the guitar solo. The vocals are the only thing that generally benefits from being done in the moment.
Check out this video of Badfinger, doing the great "No Matter What" with live vocals over the recorded backing track. It really works well. Besides, it's always a good day for some Badfinger: