"to have a good time ( = a time of enjoyment) was common in Eng. from c 1520 to c 1688; it was app. retained in America, whence readopted in Britain in 19th c." [OED]
Time of day (now mainly preserved in negation, i.e. what someone won't give you if he doesn't like you) was a popular 17c. salutation (e.g. "Good time of day vnto your Royall Grace," "Richard III," I.iii.18). Times as the name of a newspaper dates from 1788. Time warp first attested 1954; time capsule first recorded 1938, in ref. to New York World's Fair; time-travelling in the science fiction sense first recorded 1895 in H.G. Wells' "The Time Machine." To do time "serve a prison sentence" is from 1865. Time-honored is from 1593; time-worn is first attested 1729; time-keeper is from 1686; timeless "eternal" is 1628, earlier it meant "ill-timed" (1560). Time-limit is from 1880; time out in football is recorded from 1896. About time, ironically for "long past due time," is recorded from 1920. First record of timetable is attested from 1838, originally of railway trains. Behind the times "old-fashioned" is recorded from 1846, first attested in Dickens.