I give out medals fairly regularly (well, "regularly" considering the limited supply). The trust medals I'll give out to players I feel have a positive impact on the gaming environment in terms of the "playing a board game with friends" atmosphere. I give them regardless of whether someone is playing a friend or an enemy. Of all the trust medals I've given, I've only regretted awarding one of them.
I've only ever been able to award one role-play medal, and I gave that to someone who wrote an exceptional series of RPs. I've never been supplied any fun medals to award, although I've been awarded one of them myself. So I presume they're fairly rare.
Depends on which you get, I guess. I think fun medals used to be what I had the most of, but I think I gave all the ones I could a long time ago...