My grandfather's UC-Berkeley class ring was a part of him. Impossible for me to imagine him without it. Long after his death, it occurred to me that part of that may have been a reaction to the West Pointers he served with throughout his career who wore their rings all the time. Maybe--maybe not. Anyway, I bought a UW class ring probably in large part due to my admiration for my grandfather. I wear it off and on--used to wear it a lot more. I worry that it is pretentious (it is), but I still like it--and still like thinking of my grandfather.
My wedding ring only comes off when required (or when I'm fiddling with it). I can understand people who take them off to sleep, and some jobs and hobbies require that you remove jewelry, and some people have allergic reactions to the metal, but in general I agree with the line of thinking that a married person should wear their wedding ring. I guess I'm old fashioned that way.
Curiously, my grandfather didn't wear a wedding ring--just his class ring on the left hand where one would expect a wedding ring. I always thought that was weird.