Our cats go for spiders and moths or anything else that moves for that matter. The problem is when they dont look where they are going to land when leaping up to catch something.
Unfortunately as well as relieving us of nasty bugs the cats lumber us with nasty rodents. We get field voles and even on one occasion a rat released in the house and we then have to catch and release these ourselves (I am sure the cats would be happy to help catch them again but I cant watch them toying with and killing little furries). OK most of their stuff is dead but they do bring in some live stuff. The funniest used to be frogs - you would come down in the morning and find a frog happily resting in the cats water bowl.