Early to mid 1980's, if I'm not mistaken. But there were some odd-ball beverages, from small-time makers, that continued to use variations of them for awhile still longer. But for the normal sodas, I think it was the early to mid 1980s.
They disappeared in the 60's and replaced by the square tab to try to prevent the littering problem created by the tear-off beaver tails. But yes, I think there are some modern ones that have begun using them again but I don't know which.