Ohgod, I can't remember all the times I've fallen off, but here's a few highlights.
My first horse, well, not technically mine but I was riding him at my aunt's all the time. Well, this was before I had a single lesson, so it was just a hop on and ride around thing - Blaze (the horse), well he knew this and I'm sure he had so much fun with it. He was a prick to stop (as in helloooo there fence, nice to meet you, I'm going to fall off over my horse's shoulder while he turns sharply now), of course the riding bareback didn't help much.
My first major fall (out of a saddle) from Blaze was when I took him for a canter and my stirrup broke, so I just slipped off sideways. Yeah. Had to go hunt down the stirrup in the dark, too.
Second major fall off Blaze was when I was helping my cousin get some sheep in (*******s!), the girth billet broke and the saddle slipped under him while cantering. This fall is also why I never use clip-on martingales, because the breastplate didn't come off the girth when I was going down. Poor guy stood on the breastplate, which actually put enough stress on the reins to BREAK them (so you can imagine what his mouth felt like), then tripped over the saddle.
---- OKAY, so the ones above were when I was about ten. I bounced when I was that young. 8D Still, I've never broken a bone, horse-related or not.
I do remember one of my old lessons where I was told to basically drop the reins and boot the crap out of my horse to canter. Obviously, I had a bad instructor. Fell sideways-ish and scraped a chunk out of my arm on the arena fence. Another of those lessons, on a different horse, the horse did a little pop-buck and I went straight over her shoulder - this one was my fault though, because I was leaning forward.
---- HAHA, those lessons where a total waste of time and money, but I still learned a little from there.
I haven't really fallen off recently, except on a trek last year.
Day long trek - we all stop for water. My horse is between another horse and a fence, playing with the troughball. Tail flicks into the fence, which I later discover was hot. CRACK. Horse goes up, I go up. Horse goes down, I go down. Horse goes sideways, taking two other horses with her, I land in the trough. Several other riders fall off from laughing so hard. We spend half an hour hunting for the three bolted horses, have an early lunch while I dry off, then keep going.