I keep mentioning this paper to friends and can never find it, so to solve that I'll blog about it! It's a fairly readable paper on how much latency you can get away with for foldback speakers or in-ear monitors before the performers start to complain.
If you just want to skip to the results, have a look at the graphs on pages 13-15 - these plot the likelihood that a performer would rate the setup as good/fair against the latency. The highlights are vocalists will notice as soon as there's any delay, particularly if they're using in-ear monitors, while on the other extreme of the scale keyboardists can tolerate an awful lot, and other instruments fall somewhere in the middle. The paper theorizes that it's down to a mixture of how far the instrument is physically from the performer (each foot of distance is about 1ms of latency just from the speed of sound in air!), and how quickly the instrument produces sound (singing is effectively instant, while a keyboard could have a fairly laid-back synth patch).