The only power tool I use gloves with is the chainsaw. I also often use them with hand tools like an axe or a spade but not always. As @Prostheta said, tactile feedback is important. Back in the day gloves were a must when chopping firewood, nowadays not so much as I've learned to "feel" to avoid splinters digging into my fingers rather than having a clumsy thick piece of cowhide as protection.
After having read the above and giving it a thought I came to the conclusion that the chainsaw actually is the only woodworking tool that is built to fit gloves in the handles! And the lawn mower, the vibration tends to create blisters. Handheld routers, power planers, hand drills and most other electric tools all are fitted for bare hands, even the hedge trimmer despite the hawthorn thorns being quite stingy. Then again my hands are pretty large, size 9.5 or 10.