I agree with Ryan 100%. No you don't "need" them. But you just might "want" them in there.
Personally I love them. I have a big reef tank that my daughter turns her nose up at but I just started a little 6 gallon tank and she loves it. I asker her why and she indicated it was the plants. She loves the plants!
No - but a planted tank looks so much better. In the past, I had trouble growing plants, but there is so much information out there now on the internet, I view it as a challenge to relish,
getting the plants to grow well is very rewarding. And to answer your question, the plants do form part of the oxygen cycle in the tank, but with filteration and airation, it's not technically necessary.