The major change in Science Fiction is the technology, since technology has advanced so much in just a couple hundred years. This change in technology is shown in the format of the media itself as well as what is depicted in the stories. Also, the dystopian sub-genre has become more prevalent, as hope for the future has dwindled from the lofty heights when "The Great Exhibition" was put on in 1851.
Especially after the arms race and cold war, post-apocalyptic settings are common in Dystopian stories. This shows a trend in human experience that favors both armageddon and hope in equal measure.
Forbidden Planet - produced by Nicholas Nayfack in 1956, the plot consists of a spaceship coming to a distant planet to find some scientists. They only find one scientist and his daughter. It has been postulated that Forbidden Planet is loosely based off of Shakespeare's The Tempest.
Star Trek - This series is still being added onto, but it got its start in 1966 when Gene Roddenberry produced the very first episode. Star Trek follows a crew of "Starfleet", a union of different races including human, as they explore and chart space. The series is a standalone complex, which means you can watch the episodes by themselves but there is a plot interwoven throughout.
Valerian and Laureline - Started as a series of French comics, there is now a movie out titled Valerian based on the character of the same name. Pierre Christin was the original writer of the series which was published starting in 1967
Fifth Element - Starting as a French screenplay published in 1997, this also became a hit sci-fi movie. Luc Besson is the writer, having taken quite a liking to Valerian and Laureline, he wrote this screenplay with the same setting, albeit very different characters.
Fallout - Sci-fi wasn't solely a genre for written works, as Bethesda Softworks released the game franchise Fallout in 1997. The major theme of the work is redemption, as the main character awakes in a post-apocalyptic nuclear wasteland. They immediately start helping the denizens of this broken world as they explore.
Bioshock - The brainchild of Ken Levine, the head of Irrational Games. The first Bioshock game's release was in 2007. This game follows the story of a shipwreck victim chancing upon an underwater city of metal and steam. The denizens of the city are either mentally warped from genetic splicing, or in hiding. A mix between Nautical and Dystopian Sci-fi. The nautical themes are in the setting and in the design of the enemy "Big Daddy".
The Expanse - Made first as a set of novels written by James S.A. Corey, The Expanse is now a hit tv series. The first novel was published in 2011. The story is set in a spacefaring society where humans are split between three groups; those who line on earth, those who live on mars, and "belters" who work in the asteroid belt. The tv series is largely a political and military sci-fi.