Hi, I am new to this forum still and still very new to flying rc. My question is , What purpose do the capacitors serve that are attached to most electric motors on RC Planes,like my Super Cub?

They provide a little 'phase shift" to start motor rotation. They can also help reduce 'noise' from brushed motors.

They filter out high frequency radio interference, that's the main reason they are on motors and esc's for brushless motors.

ok thanks, now for my next question. How do you determine what capacitors to use on a motor? Reason I ask is because I had a very nasty crash into pavement the other day and have broke one of them off of my motor. I have thousands of these things in my storage that I got from a radio shack pallet not too long ago so I just need to know which ones to use. I would be replacing them on the stock 480 motor on the hobbyzone super cub.

Usually, the motors come with the filter capacitors with them. Or in a package for you to install, or sometimes, both. Instructions should come with the motor.

I am new to the world of RC and just bought my first plane but I am a electronic tech. the capacitor is a starter capacitor which does help the motor start turning... If you can not find any information on the Capacitor, take it to you local TV shop and they should have a capatiance meter and be able to tell you what it is and maybe even have one. It should not be to critical as long as you can get close to the value. the voltage i wouldn't worry about as long as it is a little over the battery voltage. It can have some filtering value also.....

Start capacitors are only used on single phase AC induction motors to provide a phase shift to the start winding to get the motor started. Both DC and 3-phase AC induction motors are inherently self starting and need no capacitors to run. Capacitors are also used to correct power factor in 3-phase power lines.
The capacitors on our DC model motors are strictly for RFI supression. Start capacitors are huge, hundreds of microfarads. RFI suppression capacitors are tiny, a few picofarads. I don't believe that the exact value is critical. It just needs to provide low impedence path to ground for RFI. A ferrite ring around a conductor can also act as a choke to block RFI.

B.L.E. is rite, I dont know what I was thinking at that moment.