^I was a fan of the X-Files, I've never seen Fringe.
I looked for a decent online commentary on the show that didn't have spoilers, but couldn't find one, so I'll try my hand at writing one myself.
On a basic level Fringe is a show about a special government team (mostly FBI) who investigates strange inexplicable phenomenon, much like Mulder and Scully did on the X-Files. The show takes its name from the concept of fringe science, that nebulous area in which science borders on the paranormal. The cases they investigate seem to have an inexplicable connection with cases around the globe, a phenomenon referred to as "The Pattern."
To make things even more interesting, there is a group of well-dressed bald men known as The Observers. They have no hair or eyebrows. They take notes in some kind of glyph-oriented language. Their palates have little sensitivity and so they tend to eat extremely spicey foods in quantities that would burn a hole through a normal person's stomach. Previously their appearances were extremely rare, as their primary purpose seems to be to observe significant world-changing events throughout history. In present day of the show, their sightings have increased dramatically, as if the world is on the verge of something cataclysmic.
In season Two, you start to get an idea of what The Pattern is really all about, and the way it unfolds is pretty cool in my opinion.
The major characters are as follows:
Olivia Dunham (Anna Torv)
An FBI agent, Olivia is the show's main character. In the beginning of the series she learns her FBI partner with whom she's in love has been living a double life she knew nothing about. What she discovers is not good. Later in the series she discovers that something incredible happened to her as a child that is now coming to fruition as an adult. Olivia is a study in subdued beauty. She takes her job very seriously, perhaps too seriously.
<hr />
Dr. Walter Bishop (John Noble)
Geez, what a character. During the 1970s Walter Bishop worked in a lab for the US Government that was located at Harvard University, doing all kinds of experiments with Fringe science. His enlistment in the team terminates his seventeen year stay at a mental institution. Walter is extremely quirky. His memories are fragmented and he likes to take recreational drugs like LSD and marijuana. But he loves a mystery and his scientific prowess is undiminished.
<hr />
Peter Bishop (Joshua Jackson)
Walter Bishop's son. He's got a 195 IQ but is sort of a Jack of all Trades. Initially recruited by Olivia to get his father out of the mental institution, Peter becomes a major asset to the Fringe team. He not only takes care of Walter but provides keen insights on their cases. Due to his checkered past, he has many contacts and can obtain certain things when the FBI's beaurocracy get's in the way. There is of course some hinting to a potential romantic connection between Peter and Olivia
<hr />
Phillip Broyles (Lance Reddick)
Director of Fringe Division, Broyles is Homeland Security. His first impressions of Olivia Dunham were less than favorable but that quickly changed once he saw her performance. Broyles is generally abrupt and to the point, in a somewhat militaristic fashion, but under the hard surface he's a decent human being.
<hr />
Nina Sharp (Blair Brown)
Chief Operations Officer of Massive Dynamic, the multi-national techno-corporate giant founded by Walter Bishop's lab partner in the 70s, the curiously absent William Bell. Nina carries herself with an air of smug confidence that always seems to suggest she knows more than she's telling. Nina's right arm (including her hand) is a mechanical prosthetic, eerily reminiscent of the early Terminators. Olivia is suspicious of Nina and comments that many if not most of her team's investigations seem to inevitably lead them to Massive Dynamic.
<hr />
There's a lot I haven't mentioned because I don't want to give away too much. Fringe is the kind of show that is best experienced by watching the DVD boxed sets.