I must admit I do reward my DD a lot, and it is working okay for us. I love the idea of 'intrinsic motivation', but my DD is only 8 and very sensitive, she finds gymnastics very difficult and has to work hard at it, I think she would very easily give up in frustration, so I reward her for effort. I know there are some here who would say she should absolutely love gymnastics passionately and never even think of giving up, but she isn't that kind of kid. She isn't like the tough, driven, high-energy kids I read about a lot here on CB! I don't want her to learn to give up when things get difficult, but that is what would probably happen if she didn't get a little 'encouragement' along the way. She is a moody and emotional kid who sometimes wants to give up one minute (when things aren't going well) and loves it again the next (when things go well).
She wants to do well and always tries hard, she doesn't slack off and start demanding bribes for making an effort (if she ever starts going that way, I will nip that in the bud!). It is more that she gets frustrated and discouraged and needs some encouragement. I know she should be motivated by getting the skill or whatever it is, but she can't think that far ahead as usually at that point she is stuck in feeling like "I'll never get it!". When she does well, she is very encouraged and that in itself is a huge reward for her and the extra reward is just a bonus. I don't usually reward for getting a skill, but occasionally I have for something she was really struggling with. In those cases, it is not so much a reward as a kind of joint celebration!
I don't give her money, but something that she wants, such as a book. I would never ever use a 'bribe' for getting a specific score or for something like staying on the beam. I don't think that would work for her anyway, she would already be trying her best. I understand how it can be a 'slippery slope' and monitor carefully, and sometimes we'll talk about it together. So far the rewards have been reasonable, we generally talk about it and she accepts that she can't start demanding expensive things.
As for chores, yes I do pay the kids for doing them, they get a small amount for each chore, which goes on a chart. I also make them pay for computer time, so that is mostly where their chore earnings go! I think this is a reasonable life lesson - you only get paid if you do work, and then you have to pay for things you want.