In Australia, most men (or at least the men I come into contact with) don't. I think it's a generational thing though. It seems younger men are more likely to than older men, though I confess I don't make a habit of looking at a man's hand to see if he's wearing a wedding ring. I just don't care. I suppose I would if I was in the market for a man, but I'm not. But if I was, and I wasn't sure of a person's marital status, there are fairly easy ways to find out before you make a fool of yourself by putting on a mating display.
I got married in the early 80s. My husband was adamant that he was not going to wear a ring, so I said I wouldn't either because I wasn't going to wear a symbol indicating that I was tethered to another if he wasn't, and I haven't, and I've never regretted it. At the time I was - and remain - very committed to the idea of equality between the sexes and avoiding gender stereotypes. I've never used his name, either, and always use "Ms". I'm sure other people think it's strange, but I really don't care.
Wearing a ring on your finger doesn't mean you any more committed to your partner. If someone puts an unwelcome move on you, all it takes to let them know you are not available is to tell them.