A number of people keep eels in the reef tank, some of the smaller dwarf eels do very well, and some people have even kept larger Zebra eels too. The thing is most eel will eat inverts, and some eat small fish, and they do produce a lot of waste, not to mention some of the larger ones can knock things over. If you want to add an eel then the smaller dwarf eels (golden Dwarf eel) is probably what you're look at.
The problem with any Angler fish is that they eat small fish, or anything that swims by them, so it's a risk keeping one in a reef tank with small fish.