The rule that I've always heard is that insurance is for something that you can't afford to replace if it gets lost.
So we always had renters insurance, even though we never had much stuff either - still more than we could afford to replace. We went through USAA, which is great if you have access to them.
We had a rider on my engagement ring for a while, but then I realized that if I lost it I wouldn't replace it with a similar one, so we no longer insure it. I would be sad if it were lost, but to me a new ring would just be a new ring. I'm not much of a jewelry person, though