A very common storyline is the negative aspect of science. A good portion of Sci-Fi films have an antagonist that is the direct or indirect result of humans screwing with science.
There isn't a typical type of Sci Fi story, most use different types of formats.
For example:
Alien -
Uses the similar format to a haunted house movie. People are trapped in a building/location in isolation and they're constantly teased and haunted by the monster.
Terminator (1 & 2) -
A basic chase movie.
Star Wars
A cross between Western, Samurai, Epic and other genres