Cycling gloves do a few basic things:
- reduce friction between your hands and handlebars, which could otherwise cause blisters
- dampen vibrations which might cause hand/finger numbness
- reduce pressure on your ulnar nerve, which also causes numbness
Of course, if none of these are problems for you, it's fine to ride without them. Other types of gloves should offer similar benefits too (wool gloves with "grippy" palms are nice in cold, wet weather). I try to ride without cycling gloves for rides up to an hour to toughen my palms and reduce the bizarre tan lines the gloves create. But for longer rides (especially randonneuring, which is 200km+) I can't ride without them.
What else can you use them for? Basically anything where a padded palm would help. They make great workout gloves, and I've occasionally used a pair for paddling, doing yard work or helping someone move.