How often do people reuse bottlecaps, if at all? Given the slight crease that's introduced when removing the cap, I'm a little nervous about reusing them -- though it seems that there shouldn't be a problem if they're washed and sanitized, and if there's no leakage when the bottle is held upside-down after capping.
I've never done it, and I wouldn't recommend it. I suspect that the seals inside the caps are really only good for one use.
It doesn't make sense to me to try to save money there. You just spent a bunch of time and energy making a tasty beer: you don't want to ruin it by using faulty or contaminated caps. Even if they don't leak beer, they may still leak CO2 once they're under pressure.
Or you could go with swing-top bottles. Although after some time you will have to replace the red rubber seals on those as well. But much less waste than with caps.
If you want "recyclable" caps, you could consider bottling to 1/2 gallon growlers... 38mm "polyseal" caps are machine washable and make a decent seal.
There are also twist close plastic bottles and caps, the kind that come with the "Mr. Beer" kit, that are reusable.
I have reused them with NO troubles! Just re-sanitize. I don't make it a regular practice though. Only when I run out of caps when bottling!!!!