When I was a kid, Jason Voorhees was pretty much the end-all, be-all of horror movie psychos. Freddy Kruger and Michael Myers were cool, but neither was quite as iconic as Jason. To this day hockey masks and the very name "Jason" can bring up images of a machete-wielding psycho in many peoples' minds.
The Friday the 13th movies can arguably be called first really huge horror flicks. Psycho, Night of the Living Dead, and other movies had helped bring horror to the mainstream, but nothing could top the sheer popularity of the Friday the 13th franchise. In fact, it's considered one of the most successful American media franchises in history. Its popularity still strong today; they recently made a "reimagining" of the first movie, which has become the second highest-grossing film in the series.
What is it about the Friday movies that made them so popular?
For starters, there's the setting and environment: a campsite by a lake out in the woods. There's something really intristically scary about camps. Out in a forest filled with strange noises and mysterious shadows, away from society (and help), where you are dealing with forces much more ancient than you. Not to mention there's just something unsettling about the camp songs, bright decor, and cheerful counselors. The same counselors that are supposed to protect you...
Ah yes, the counselors. I was a camp counselor myself for a summer. As one can imagine, putting a bunch of teenagers out in the woods tends to lead to some rather mischievous behaviour. The counselers in the the Friday movies just can't seem to keep their clothes on (and who can blame them, there's some good-lookin' people in these movies).
Thus, we have the motivation for our hero, er I mean villan. Jason's on the warpath to avenge his mom and get back at those slutty kids. Nothing like a moral crusade to get the audience rooting for a killer - yeah, get those naughty hoodlums!
Then there's the man himself and his iconic hockey mask. A huge, remorseless, silent, seemingly-immortal killing machine. His image is so strong that many people don't realize/remember that he was barely even in the first movie, and he didn't pick up the mask until about halfway through the third. Jason's mask has "become one of the most recognizable images in popular culture" (from the wiki).
There's quite a few more sequels, despite the fourth one being called "The Final Chapter" (not to mention the one in 1993 called "The Final Friday"), so I won't list all the trailers here, but I will include the one of the new remake (I have not seen it yet, but it does look promising).