Best performances on a talk show?
 

Stacked Dead Actors - Foo Fighters (SNL)
Cochise - Audioslave (rooftop performance on David Letterman)
Spiders - System of a Down (Conan O'Brien)

Rage against the Machine - performed on SNL, Conan, Letterman (outdoor concert in front of Late Show building in the rain!)

Incubus - first appearance on Letterman.

since SNL was mentioned, even though it wasn't ever a talk show, I'd have to go for Elvis Costello when he stopped the entire show four bars into "Less than Zero". Seems the record company wanted him to play "Less than Zero" because it was a popular single, to his objections.
So he stopped the show, and started "Radio, Radio", which is about Radio controlling it's listeners.

High class.
Linkage: http://www.ecostello.com/audience/990906.shtml

Any Aerosmith song. Period.

Re: Best performances on a talk show?
 

The Guerilla Radio performance on Letterman kicked ass. Tom Morello proved he didn't use any of that software synthesized stuff. Just him and his killswitch.

Funny how they had to bleep Zach's F word lyrics on Letterman. Had to do the same when Chris Cornell of Audioslave sang "Set this f*cker off" from the rooftop. Haha.