I have a modereratly planted tank without any bubbles. I have never had a problem with there not being enough O2 in the tank. This is because plants, during the day emit O2, and eat up the CO2 in the water.
There is alot of debate of plant forums about the use of air stones. This is becuase the people on those forums tend to have lots of plants and advanced CO2 systems in thier tank. Many people will run air stones at night to increase the O2 in the water. This is because while plants absorb CO2 and emit O2 during the day, at night, when the lights are turned out, the plants do the opposite. Some people with heavily planted tanks use air stones all day without adverse affects on their plants. Most of the people with heavily planted tank do something to aggitate the water at night.
IMHO, if you are not injecting CO2 and your tank is not heavily planted, and you fish are not gasping for breath, then you will not need an air stone. That doesnt mean you can't have one though.