I've had several species (with multiple species per tank) and a friend used to as well.
In general, morays aren't really aggressive - just predatory. If it's not bothering them and they can't eat it, they usually leave it alone. There are of course exceptions - any individual fish can be an exception, and some species are generally nasty.
Gymnothorax moringa might be the most aggressive fish I've ever seen. Definitely recommend avoiding this one. They're not "commonly" found in the hobby, though when they are found, they're usually cheap and this is why. They will harass everything, regardless of size - including your hands, and they're not above coming out of the water to do it.
G. eurostus (in my experience) has somewhat similar temperament, though not quite as extreme.
The Caribbean/Atlantic Muraena species aren't *generally* aggressive (are more so than most species, though) but they don't particularly like anything with similar patterning. I had to get rid of a M. pavonina because it was going after my Whitemouth (left everything else alone), and the recipient of that one had to pass it along too when he got a M. melanotis and the two didn't get along.
Other than the above, as long as there's plenty of room, I would expect most morays that don't look like each other and can't eat each other to get along fine. Some don't even seem to care about same/similar species - not personal experience, but I've heard of people keeping multiples of G. miliaris or the various Echidna species with no issues.