I'm mostly libertarian, although I'm sure the more pure libertarians here would call me a fuzzy-headed socialist.
Anyway, for seatbelts:
Be careful comparing rich, Western countries to poorer countries. As we get richer we value personal safety more, so we demand things like seat belts and air bags in our cars.
I believe that our politicians see that demand, then jump on the bandwagon and pass laws that basically everybody thinks are a Good Idea, and then take credit for making us safer.
I'm not 100% certain that is true for seatbelts; I haven't actually looked at the graph of traffic fatalities over time, to see if there is a bend in the curve when seatbelt legislation is passed.
For smoking: we shouldn't be allowed to do things that hurt, or have a "reasonable" chance to hurt, other people. Personally, I waffle back and forth over whether second-hand smoke imposes an unreasonable chance of harm on others.
I've looked at the evidence, and it seems that only people exposed to repeated, long-term secondhand smoke have an increased risk of death. Like spouses or children of smokers. And the smoking bans NEVER apply to private residences. So again, I think politicians may just be jumping on the bandwagon and passing feel-good laws that do no good (although in the last couple of days I read that it looks like grotesque images on cigarette packs ARE measurably effective at reducing smoking).
For vaccinations: "herd immunity" from vaccinations is a true "public good," in the strict economic definition of "public good." I think it is fine and dandy for the government to provide true public goods, either directly or (usually better) by supporting/subsidizing private industry. Follow this link for a reasonable, very-smart, mostly-libertarian perspective on public goods.