I don't want to brag or anything, but i've taken thousands of feet of leader-falls over the past 10 years. Tons of air-time on sport and trad, some on mixed routes, even some on high-ball boulders, but never on a screw. I've experienced a few 40+ footers with the biggest being around 60 ft. (i didn't get out the tape measure) The only injury i've recieved was a couple broken bones in my foot. I came in a bit funny, thats it.
Now i'm not saying that you should go out and whip away, but if you whip it doesn't mean you're gonna die. And I've found that that is the key, RELAX! YOU'RE PROBABLY NOT GOING TO GET HURT!
Here is a couple of pointers;
1. if you fight the fall until you are already airborn, you've just managed set yourself up for a bad one.
2. Don't push off too hard (you'll swing back in too fast) and don't just go straight down (cuz' the rock will stop you before the rope does). Once you start getting gripped, just glance down and get a quick survey of what's below you. i.e. ledges, corners, your last piece, etc.
3. It helps if you know how to fall. (Years of skating and biking on a half-pipe, snowboarding, mountainbiking and doing flips off of rope swings and bridges as a teen helped me with that). So if you were a fat kid who's only falls were while standing on a stool to reach the cookie jar, don't whip more than 3 feet!
4. Remember! Ropes don't fail, nor do carabiners or stoppers or Cams or bolts or belay devices. If you have done everything correctly, everything will work correctly. You have to have faith in your climbing ability and your ability to set up a system that won't fail you.
So what goes through my head... I'm already thinking about pulling my rope and doing it again, because i'm confident that i'll be okay and back on the route within minutes.