This is relative depending on your subject. Slow motion for a person walking could be 60fps while a car may be 1000fps. Both of these are examples of the capture rate. They are captured at this rate and then replayed around 30fps.
Determining necessary frame rate: Think of your subject's action that you want to slow down. If it's a drift in a car, lets say it took 1 second for that car to come around the bend. How long would you like it to take in the video? 2 seconds? 60fps. 4 seconds? 120fps. You simply do the math to determine what fps you want to capture.
You'll find that the most popular DSLRs (and helmet cams) are going to capture at 60fps. Usually this won't meet your needs of slow motion. To compensate, many professionals are using a software solution that is much cheaper than a hardware solution. Twixtor is one of the leading models and has been able to slow some videos to the equivalent of 2000fps (remember, playback is always around 30fps) from a 60fps capture. I say "some" because the software is attempting to determine what occurred between the missing frames and this can cause artifacts. If you're shocked by the sticker price of Twixtor, take a moment and research prices of cameras that capture at the rate Twixtor can almost duplicate, at 1080p, without having to carry that price tag around potentially dangerous areas. Then try and strap one of those cameras to your bike/wakeboard/car.