Sitcoms can be shot two ways: live, in front of a studio audience, or filmed and edited together. In the later case laugh tracks are added in post production where desired. Desi Arnez, with I Love Lucy, created the former, filming the sitcom live like a stage play and editing the film together after the episode was shot. Advanced in television production later allowed for "real-time" editing by switching cameras and recording shows live… on video tape.
The laugh track was first used with the sitcoms that were filmed and edited together, but later was used to "plus" or "juice" the laughs for shows filmed in front of a live audience. Some sitcoms use their own custom recorded tracks (like, i believe, Chuck Lorre's sitcoms) while most rely on library tracks – hence you can hear the same people laughing on Happy Days in the 1970s are laughing at Everyone Loves Raymond in the 2000s.
As others noted, the "documentary sitcom" as originated by The Office is now the norm, with no laugh tracks, but this trend actually started in the 1970s with MASH. In the show there is no laugh track while the characters are in the operating room (the producers thought that would, rightfully, be in bad taste) and after the first few seasons the laugh track was removed all together. You could say that was around the same time the show stopped being funny and became maudlin, but that's another question…