Aboard the Jupiter Mining Corporation vessel Red Dwarf, Dave Lister, a lowly 3rd Technician, smuggles aboard a pregnant cat and when he is found out he is confined to suspended animation for refusing to surrender the animal to the captain. During his time in stasis his bunkmate Arnold Rimmer, a lowly 2nd Technician, is forced to perform the maintenence duties without Lister's help and inefficiently repairs the drive plate, causing it to blow and subjecing the entire crew to deadly radiation. 3 million years pass until the background radiation level has dissipated to a safe level. At this point Holly, the ship's computer, releases Lister from stasis and tells him of the accident and also ressurrects Rimmer as a hologram to be a companion for Lister. After the initial shock, Lister realizes that he has the run of the ship, allowing him to be, basically, himself: a layabout slob. Rimmer and Lister discover that the cat had been sealed in the ship's hold during the accident and has bred there for the last 3 million years and evolved into man, one of whom is still on the ship. The rest of the cats mistook Lister's laundry list as navigation instructions to a habitable planet and crashed and died in space. When he discovers his new friend, Lister decides to complete his dream of owning a farm on Fiji and orders Holly to set a course for Earth. Much of this first season involves Rimmer trying to still boss Lister around even though he is just a hologram, the cat coming to grips that he is the last of his kind alive, with Lister constantly trying to get Rimmer to "turn himself off" so Lister can keep company with Kochanski's hologram instead. This is because the ship can only support one hologram at a time. Kochanski was the attractive officer Lister was in love with before he went into stasis.
The main dramatic thrust of the series from this point forward is Lister's attempt to get back to Earth. Along the way, however, are frequent distractions that usually see the Dwarf crew encountering strange races and lifeforms that have developed in the intervening millions of years. However, a core tenet of the series is that there are no aliens anywhere in the universe -- every element of the large and bizarre mix of intelligent life within the Red Dwarf universe is in one way or another derived from Earth, which is a result of developments in robotics and/or genetic engineering.
The crew roster changes as the years go by. During the second season, the Red Dwarf crew encounter the sanitation mechanoid Kryten, rescuing him from a long-since crashed vessel. Initially, Kryten only appears in one episode of Season 2, but by the beginning of Season 3 he has become a full time character in the series. At the end of Season 5, disaster strikes when Lister loses Red Dwarf, having forgotten which planet he parked it on. However, we later learn that Red Dwarf was actually stolen. This forces the crew to travel in the smaller Starbug craft for two seasons, with the added side-effect that they lose contact with Holly. In Season 7, Rimmer departs the crew to take up the role of his alter-ego from a parallel universe, Ace Rimmer, whose name has become a legend and a legacy passed down from dimension to dimension and is everything Rimmer ever wanted to be. Shortly afterwards, the crew find a replacement for Rimmer when they encounter another parallel version of themselves. In this universe, it was Kristine Kochanski -- Lister's long-time crush and ex-girlfriend due to merged realities -- who went into stasis, while Lister died and was brought back as a hologram. A complicated series of events leaves Kochanski stranded, and she is forced to join the crew.
Finally, in the eighth season, Red Dwarf itself is reconstructed by Kryten's nanobots that had stolen it and broken it down into its constituent atoms. In the process, the entire crew of the ship -- including Rimmer -- are resurrected, but the Starbug crew all find themselves sentenced to two years in the ship's brig on a set of convoluted charges. The series ends, however, with Red Dwarf being eaten away by a virus and all on board evacuated, save for Rimmer who is left to face Death, in the form of The Grim Reaper, for the second time. Unhappy with his predicament, he knees Death in the groin and runs away -- although the cliffhanger ending leaves this open to interpretation.
I really thought that the first five seasons of Red Dwarf were the best. I didn't care for seasons six and seven that much when the crew was traveling in Starbug. The good part of season six is that the role of the Cat was significantly increased to great comedic effect, although the trade-off is that Holly's antics are sorely missed. In season seven Rob Grant, half of the team that had created and written all Red Dwarf episodes, left the show and there was a clear downturn in quality and imagination. Kochanski's addition could not offset the loss of Rimmer, and the show just lost something. Season eight was better, since with the entire crew restored, there was more opportunity for character interaction under completely new circumstances. Chris Barrie is back as Rimmer, and this was certainly a welcome change. In spite of the fact that I am not crazy about seasons six and seven, I would still recommend the entire collection to anyone. It is far funnier and more original than almost anything else you'll ever see on television.