The Friday the 13th series ran from 1980 to 2003 and chronicled 11 (count 'em, 11!) different murder sprees committed by the Voorhees family. The fact that they were all minor variations on the same film (eg. "with a telekinetic girl like Carrie", "in New York", "with a body-jumping hell-worm that likes to kill", "in space") didn't matter to fans - all that mattered is the films were creepy, the cast was young and there'd be a series of gory death scenes. Truth is, these films weren't very good - or gory, on the whole - but they were tremendously influential and anyone with any serious interest in horror should watch a few, preferably early, films in this series.
I won't make any attempt to be a definitive text or knowledge on the series - most of them were made by unenthusiastic cast and crew people against their 'better' knowledge and taste. As such, production stories are largely uninteresting or irrelevant. If you do want to know more - for example how to make your own independant horror hit and sell it to Paramount - I recommend getting a copy of the Region 2 (UK) Warner Brothers release of the first "Friday the 13th" with it's excellent feature documentary and a copy of "Crystal Lake Memories: The Complete History of Friday the 13th" by Peter M. Bracke , a very well-researched hardback detailing the productions of all the Friday the 13th films, in depth and with interviews. There's a great online resource here at Camp Blood too.
1980 - Friday the 13th
1981 - Friday the 13th Part 2
1982 - Friday the 13th Part 3
1984 - Friday the 13th: The Final Chapter
1985 - Friday the 13th Part V: A New Beginning
1986 - Friday the 13th Part VI: Jason Lives
1988 - Friday the 13th Part VII: The New Blood
1989 - Friday the 13th Part VIII: Jason Takes Manhattan
1993 - Jason Goes to Hell: The Final Friday
2002 - Jason X
2003 - Freddy VS Jason
2009 - Friday the 13th (remake)