Nirvana on TOTP... they weren't allowed to play their instruments but Kurt was allowed to sing, resulting in this:
Muse on Italian TV... they were told to mime, so they did. The singer is now the drummer, the drummer now the singer and bass player, the bass player now playing lead guitar. My favourite bit is where Matt points the drum stick at the camera and he zooms out like it's some sort of cool effect

Oasis on TOTP... again not happy with having to mime, Noel and Liam switch places.
All ABout Eve on TOTP... not really screwing around but apparently they couldn't hear the audio, despite the fact the TV audience could. Leading to this awkwardness
There's also this one from Iron Maiden where they seem to all take turns singing and sound exactly alike. The crowd doesn't look thrilled:
http://www.kontraband.com/videos/19426/ ... iden-Mime/