First off, it's good to learn to run out of tricks. This is where you try something, and the board goes wrong, and you catch yourself running. It takes some getting used to, but if you do this right you'll get out of a lot of falls!
Second, learn to not catch yourself with your hands. Your natural instincts when you fall are to throw your hands out, but when you do this on concrete from a skateboard, you'll break your wrists.
You can buy wrist guards for skateboarding, and if you are afraid of catching yourself with your hands these can help, but I think it's better to force yourself to learn to fall differently.
When you fall, roll to land on your shoulder or back instead, tucking in your elbows. You might want to actually practice this a little! Go out to your yard, or someplace sort of soft like that, and stand on your skateboard. Then simply fall forward, and roll to land on your shoulder. If you can, roll with the fall - land on your shoulder and let the force of the fall play itself out with the roll. It'll hurt a little, but not that bad.
If you are skateboarding on ramps, then kneepads give you a great way to fall. You want to teach yourself to always fall to your knees, and slide down the ramp. You can actually practice this, and it's fun, too. Just run up the side of a ramp, drop to your knees and then slide down. If you are skateboarding on vert ramps, then get a good running start and get as high as your can before dropping. Practice like this for a while, to get it in your head.
Falling is a big part of skateboarding, but if you learn to minimize the damage from your falls, and wear a helmet and pads, you should be OK for the most part. Check out reader's stories about their worst falls and share your own over at Readers Respond: Worst Skateboard Bail Stories!