Many have seat belts. Kennywood's 1921 Jackrabbit has authentic leather seat belts. (Made with fresh strong leather) SFA's even older Wild One has seat belts, but they are modern belts in modern cars.
At the other extreme in roller coaster history, all of the Intamin hypers have seat belts.
I would guess that most coasters today that do not have OTSRs do have seat belts.