Common problem...
Sorbut said:
only two options I know of - use BMX style pedals with lots of grip. they will cut your shins to bits if you do come off though, or go spd type clip ins (clipless). Just use very light settings. What you describe I experienced and its dangerous particularly on jumps. No issues with spd pedals and this falling over thing never happens if you set the springs light.
solved by four methods:
1) flats with pins and bmx style shoes(but watch your shins even more. the cost for a good set varies from about $25 on up).
2) toe clips(old school, but work pretty well and some folks still swear by them. fairly inexpensive, but the clip can be a pain to get into in you need to restart on bumpy sections)
3) power grip(I think that's the name. it's a strap that attaches to your pedal and you slide your foot underneath. those that use them swear by them and they're not that expensive.)
4) clipless(should be called clipins, but the name refers to the lack of toe clips not how they work. most expensive as you need special shoes. they work the best at keeping your foot attached to the pedal with zero effort. the drawback is that it takes time to learn how to use them properly and you will likely fall while learning. most who use them wouldn't dream of using any of the others, but there are some who give up after a while).