Generally speaking, just owning and using an emulator is completely legal in most places. (I won't say everywhere, because some places actually have strict laws about how any general purpose computing devices can be used.) But it also sort of depends what we mean by "emulator".
If we mean the sort of emulation software and systems we used to play with old software and ROMs then, as pointed out already, the legalities often centre on the intellectual property laws around that software or ROMs.
But it's not too much of a stretch to think of something like the Java "look and feel" as GUI emulation (Sun certainly did in some documentation). Microsoft also decided that emulating their UI in Java Swing was in conflict with their ownership of the UI.
Thus, emulation of the Windows look and feel in software created with Java and running in a JVM was restricted to VMs running on Windows. That is, the JVM disallowed apps from switching to the Windows look and feel at runtime if that JVM wasn't running in Windows. I admit this might be more of a trademark issue. But I think it highlights where things like rights and ownership sometimes take you.
Perhaps this is beyond the scope of the question, but it is often useful to be reminded that the law is simultaneously subtle and blunt sometimes, and decisions often turn on specifics of the language used.
I recall there was a very hackable programmable calculator platform that both emulation and writing your own apps for is essentially forbidden, and the rights holders are particularly litigious on both accounts. And they have used the "emulating our stuff is the same as using our stuff without permission" argument with some success. Well, where success is measured as "some courts have found in our favour" or "we scared away interested hackers and squelched further development."
Whether or not it is a good idea is another thing altogether.