I wear one when rock climbing, kayaking, snowboarding, skiing, motorcycle, bicycle, skateboard, football, etc. Pretty much any time I go over 8mph. I even considered one in aussie rules football but they were hard to find in the states.
I found that helmets for winter sports are better than hats. They don't soak up sweat like a hat does so do better in cold and are better vented than a hat as well. They also really help with the trees.
It's also interesting that they used to be "nerdy" on ski slopes in the US, then several major states required everyone under 18 to wear them. Now 80% (feels like) of kids wear them all the time, so you actually look wierd if you don't wear a helmet.
I definitely wear them on bikes and have needed them (and bounced off of them) many times. I tend to tuck when I go off the bike so I bounce the back of my helmet. There's a heart warming sensation of relief when you hear that hollow thunk sound of the helmet taking the blow on the pavement, tree, hardpack, rock, etc, with no bad effects on you.
Also on my commute I tend to hit 45 mph multiple times in the first 2 miles (I drop 500 ft in 2 miles and I feel it's safer to do 35 like the cars on the nicely paved winding suburban road than to sit in the bike lane).
Finally... I made this guy (who hates helmets) put one on after the kite pulled him up into the goal posts on a previous run. https://www.youtube.com/watch?v=9PGKG5ZFMQg He thanked me a year later.