The only insects I've caught with intent to keep caged up are...dead ones. Or maybe not quite dead ones, in the case of the cicada shell that I still have closed tight inside an empty film canister. Though I do wonder where the dead moth I found (in a pool) that I kept in a baby food jar ever went off to.
Anyway, in regards to live ones, I've only caught them to see if I can, they get released right away. I've done this to butterflies, lovebugs, oh I can't even remember what else...I've picked up pillbugs before just because I can. I think it was mostly butterflies I chased after though. And this wasn't with intent to catch, but I did manage to coax a dragonfly to sit on my finger for a few moments one time. I was utterly amazed at that.
If there were fireflies where I used to live, I probably would have tried catching those too, but alas, there were none. I would do so now, I'm always tempted to whenever I see them around, but it would look just a little bit weird ah ha.