Throughout the years I have been keeping fish, I have found that the telltale sign of oxygen depletion in the water is when fish start breathing heavily, i.e. opening and closing their mouths constantly. Of course, other factors such as toxins would also make them do this. However, if your fish don't keep opening and closing their mouths, they are getting enough oxygen.
Having said that, increasing the amount of oxygen in the water doesn't hurt. During the summer months when your water may get a little warm, the oxygen levels will drop in water. If you medicate your tank, the oxygen will also drop. If you find yourself having an algae problem, oxygen levels will also drop. There are quite a few factors that would warrant having an air stone/bubble strip running in your tank.
Make sure that you set your filters up so they are creating a lot of surface agitation. I wouldn't say that an air pump is a necessity, it's just something I would advise people to have at hand if you ever need one
