Bees, wasps, hornets, and any black and yellow flying insect that looks like one.
I've had it long before I ever got stung (which wasn't so painful after all). I can still point out a place where I saw a bee once near my grandparents' garage (back in, like 1963 or so) which I avoided for years.
Last summer bumble bees were getting into my basement and hanging out near the window by my work bench. some were alive, but about 1/3 of them were dead on the floor. I came up with the scheme of sucking them up (dead ones and living) with a shop-vac with an extra couple of extension tubes on the hose. Worked even better when I added an inch of soapy water to the canister, so they drowned almost as soon as they hit the bottom. That way, I was able to empty the canister without wondering if there were going to be some PO'd live bees waiting for me inside. I was collecting anywhere from 10 to 20 bees each day for a couple of weeks with the shop-vac and a strong flashlight, then nothing. None this year either.
I don't mind spiders (even in the house), as long as they stay off me. I figure they're just doing their job of catching flies and mosquitos. I would never pick one up. Most other insects and arachnids either, but I wouldn't jump up spilling my coffee to avoid them like I would for bees.
On the other hand, I have no trouble handling houseflies, caterpillars, fireflies, ladybugs, ants, and small hermit crabs.
I used to be able to climb trees and (later) towers, but about when I turned 35, I just could not go any higher than about 40 feet, even with a safety harness and safety rail inside a triangular tower. One day I tried going up about four times. I'd be on the ground, look up, and say, Okay I'm surrounded by the tower structure, I've got this harness on, which is clipped to a rail on the ladder that stops you before you drop a few feet, and I could go totally limp and nothing would happen to me. I had done it before, with less safety equipment, on the outside of a higher tower, but this time I'd only get to 40 feet high or so, and I'd have to go back down. Once I got on the ground, I could not remember what was so bad about the height, so I'd start climbing up again. Reach 40 - 50 feet, I freeze again, and go back down. Four times in a row.
I'm fine with aircraft, balconies with decently high railings, glass elevators on the outside of buildings, and I'd probably try hang-gliding too. Jumping off a ten-meter diving board (into a pool of water, of course) is my idea of a good time, but maybe that's because it's just under my limit.