I'm proud to say that I don't.
I've got a 6mm Rem, for paper and maybe deer some day. I guess one could say 6mm (.243) is a bit of overkill for paper, but then anything but a pellet gun is, really.
Then, I've got 3 22LRs, which aren't really overkill for anything, except that I've got three of them. One is a single-shot heirloom piece. That doesn't count.
I bought a 77/22 because I wanted a repeater that could handle a scope and be very accurate yet also beautiful. Great paper puncher, I used it on a squirrel once, and it blew half his head off, so I guess a pellet rifle would have been OK there, but it wasn't gross overkill either.
I bought a Marlin 60 used last week. I missed the semi-auto 22 I used to have. This should be a great plinker. It isn't really overkill for anything.
I have a Marlin 1894 in 44 Mag. I intend to use this for targets, 3-gun competition, and maybe deer. I don't think it's overkill for any of those. I wouldn't take it squirrel hunting, I don't think.
I do have a Ruger Redhawk in 44 Mag that I intended to use as a deer gun. I use it now only as a target gun. But even that is not overkill, as I handload it pretty lightly. (185 gr. bullets, light charge of non-magnum powder) It feels like a 38. That's not a rifle though, my bad.