How corporeal do you think ghosts are?
Can they sleep?
... I think those are the two most pressing questions I have.
Since ghosts can't taste, I get the feeling that they're not corporeal beyond being able to reflect light and be seen, and affecting flesh to make it feel cold. We know poltergeists are something else entirely, as they can actually interact with solid objects, but I don't think ghosts can (Nearly Headless Nick had to coerce Peeves into causing a ruckus for Harry once, which suggests he couldn't do it himself).
As for sleep, I doubt ghosts have the ability to do such a thing anymore. It may be an affectation to act as though they can, but I think sleep is something that requires a physical body that can get tired and requires sleep to repair itself. Makes choosing to be a ghost sound less and less attractive.
I got the feeling from the books that ghosts have relatively the same mental capacity as they did when they were alive, and they seem to possess all of the five senses (except for touch) to some extent (I believe Nearly Headless Nick at one point said that they brought rotten food to his death-day party because if it's a very strong smell then they can taste it.) Though I had sometimes thought that they had the power of telekinesis, but since Nick had to get Peeves to make a bunch of noise for him (as well as breaking the vanishing cabinet) so it doesn't seem like they can do that either.
Sleep? I have an odd recollection of Binns falling asleep midway through a lesson at one point? I think they can, but it would be more like a light doze, and that although they would be capable of it they wouldn't actually need it, since like Acacia said they don't have a physical body that can get tired and need to repair itself. Yeah, I don't think I'd want to be a ghost myself ...