Similar in ways to the easy bunker thread.
I'm going to assume that slow play is not an issue, and that we're only talking about ideal playing conditions.
Ideally, my rough criteria is very similar to my bunker criteria. I like the rough to be deep enough to yield a variety of different lies that the golfer must correctly interpret, from "flier" to "pitchout". Actually, it's really fun when there are lots of flers late in the summer, but that's pretty easy scoring conditions. Similarly, late spring conditions, when the rough is wet and dense, requires brute strength, is more difficult, and less fun.
The grass type makes a huge difference. Poa makes crummy rough. It yields few fliers, and offers less resistance than other grasses. The rye grass rough at Pumpkin Ridge can be very tough at 2.5 - 3 inches in the summer. It can really fool you. Sometimes the ball goes nowhere, or worse yet the club turns over, on an innocuous looking lie. Obviously, bermuda and kikuyu, which I'm less familiar with, are particularly nasty for their length. At Kinloch, they have 4-5 inch bluegrass rough, which is very difficult, and almost always requires extra club and conservative play.
In general, 2-3 inch rough seems about right for your typical golf course. But 2-5 inch dry fescue, where a downwind flier lie goes forever, and a shot against the grain never gets to the target, is my favorite.