I haven't checked out X Files since it scared the crap outta me when I was a kid. I did see both movies and enjoyed them, though, so I may give the series another look, considering how many comparisons Fringe got to it.
People who haven't might want to check out Lost, if they like the serialized aspect of Fringe- you have to start from the beginning with this one, though, there really aren't any stand alone episodes, all the episodes are chock full of mythology to pore over and theorize about. Plenty of easter eggs as well.
In terms of movies, people might want to check out 12 Monkeys and 28 Days Later. They both feature a dystopia and have sci-fi elements to them that Fringe fans may enjoy.