1) 2001: A Space Odyssey
One of the most influential sci-fi films of all time came about when director Stanley Kubrick got the bright idea to adapt Clarke's story The Sentinel. 2001 went on to inspire everything from Alien to Solaris. His sequel, 2010: The Year We Make Contact, was also adapted into a movie. Only two more years till we see if it's true!
2) Steven Spielberg
This geekboy adored Clarke's work so much, it inspired him to make films like Close Encounters of the Third Kind, E.T., and A.I. (with fellow Clarke devotee Kubrick). So Clarke pretty much made Spielberg's career. Now you know who to blame if Indiana Jones and the Kingdom of the Crystal Skull sucks.
3) Warp drive
The special effect used to create the stretching of the U.S.S. Enterprise on Star Trek: The Next Generation when it entered "warp drive" was achieved by a process known as "slit-scan photography." The process was created by F/X guru Douglas Trumball on 2001. Trumball also went on to do the effects for Blade Runner.
4) Cell phones
In 1945, Clarke wrote a paper explaining how geostationary satellites (in space!) could be used to make huge leaps in telecommunications. Turns out he was right. The next time you complain about poor reception, remember that you wouldn't even have that RAZR without Clarke.
5) Monkey butlers
Clarke also believed that, by studying animal psychology, we could eventually use chimpanzees to solve our labor problems, even using them as household servants. What? You don't have one?