Do Guitar Hero peripherals work with Rock Band and vice versa?

I own the Guitar Hero instruments. Can I buy a Rock Band game and use the instruments from Guitar Hero to play the game? And vice versa?

It depends on the instruments.

Here is a really nice compatibility chart that I found when I had the same question.

As JustinP8 pointed out, you can also check here:

http://www.joystiq.com/Instrument-Compatibility-Matrix/

But there's no need to read that, as long as we're talking about a game released in the last 2 years or so, all the plastic instruments are broadly cross-compatible and work in either game — microphone, drums, guitar. Pick Rock Band instruments, pick Guitar Hero instruments, everything "just works" in any rhythm band game.

However.

You do need to be careful on drums, because the 3 pad / 2 cymbal arrangement of the Guitar Hero drums makes 4 pad Rock Band songs all but unplayable.

http://www.fakeplasticrock.com/2008/11/guitar-hero-and-rock-band-drum-compatibility/

Remember that GH supports a 4-lane drum pad mode, but RB does not support a 5 lane mode, nor will RB3 "pro mode" 4 pad / 3 cymbal drums support GH's oddball 3 pad / 2 cymbal arrangement.

So if you plan to play drums in both games, I strongly recommend you get a Rock Band drumset only.