I saw some dude with a "Buckle Up" bumper sticker on his truck, presumably encouraging random other people to wear their seat belts. I can understand why the state would want people to be more well protected in their cars, but I don't know why individuals would want other individuals to buckle up. I do understand encouraging your friends and family to buckle up because you derive utility from their well being.
As far as other people go, I'd rather that nobody else on the road with me was wearing their seatbelt. They'd be safer drivers if they took off the safety belt. In The Armchair Economist, Landsburg suggests that roads would be the safest if everyone had a spear pointing out of their steering wheel straight at their heart. Imagine how safe you'd be in that precarious position. The fact is that seat belts are a form of insurance and wearing them causes moral hazard...people are willing to do crazier things when they're wearing a seat belt compared to when they aren't wearing one, and that raises the probability that they'll be in an accident (with you!).
The same moral hazard problem is present in cyclists. One study found that cars pass helmeted cyclists with 3" less space than riders not wearing helmets. Also, a cyclist is more likely to pull out in front of cars or do something else stupid if they're wearing a helmet because they'll be more protected in the case of an accident (thus reducing the helmeted riders' costs of taking the action while the benefits are the same for riders with and without helmets).
So, I might make a bumper sticker that says: "Please don't buckle up." Actually, I probably won't do it and I don't put bumper stickers on my car anyway.