A lot of people have open topped tanks. Reef tanks for example are frequently open topped with lighting suspended. People who grow plants which extend above the water often do the same.
A lot depends why you want to do it. The type of lights required for these two scenarios for example, is quite different.
Things to remember with open topped tanks include the fact that a lot of fish jump, and you risk loosing fish that way. Evaporation is usually higher. Dust and other airborne contaminants get into the tank more easily.