I think it generally went like this:
60's and earlier, mostly cloth
Late 60's and 70's, cloth and cello type tapes dominated
Early 80's to mid 80's, vinyl padded tape in all colors was the rage (especially in white like the pros preferred).
Mid 80's to 90's, "cork" in all colors jumps in the mix with vinyl padded tape
Mid 90's to present, tacky synthetic (silicone?) tapes comes in to join "cork" (in parenthesis because I'm never sure if all of them are synthetic or real cork). I think vinyl padded tape can still be found but less and less of them around every year.