To decide if you need an air pump for your aquarium you want to look at the other pieces of filtration that you have and determine whether or not they are sufficiently providing oxygen for the aquarium.
I like air pumps on fresh water aquariums. They're great at supplementing oxygen into the water. Most fresh water filters don't do an adequate job at adding air or oxygen to the aquarium simply because they're cannister style or they're hang on and they just don't agitate the water enough to really push oxygen into the water. As your fish grow the oxygen demands are going to increase as the fish get bigger.
Also, when the water warms up in the summer the water has a lower capacity to hold oxygen, so an air pump is going to be very beneficial to add that extra air that's needed. Dissolved oxygen is very, very important to fish, to bacteria, and even to plants at night. Plants and algae need oxygen at night.
So air pumps are relatively inexpensive. They're pretty quiet nowadays. And I don't see any reason not to have one on a fresh water aquarium. Again, on salt water your filtration should be stout enough to not require the need for an air pump.
But, once you do go with an air pump, you want to make sure that it's installed properly. If you have your air pump located below the aquarium and the power goes out it's possible to create a back siphon of water through the aquarium line into the air pump, and it'll result in siphoning all the water from your aquarium onto the floor. You can avoid this by going with a very inexpensive two to three dollar check valve that will go inline on the air line from the pump to the air stone in the aquarium.
Other things to consider is the type of air stone. There's air stone that will produce fine bubbles and ones that will produce coarse bubbles. Depending on the needs of the aquarium fine bubbles will give you a little bit more surface area, and that's going to give you more oxygen. But sometimes they don't break up as easily and it'll result in water that looks a little bit cloudy.
So I like nice, thick, coarse bubbles, and four or six inch air stone works great. Put it behind a rock or a plant and it creates a very nice visual look to the tank while adding critical oxygen to the environment. And keep it on all the time. Keep it on 24/7.