X Files
Buffy
Angel
Don’t name Sci Fi shows- I only want shows in which THE SAME group of people in our world deal with/fight on a regular basis strange/paranormal/supern. things. And by THE SAME group, you know I mean shows where we follow the same group through stuff, not shows where strange stuff happens to different people each episode (Twilight Zone, etc.).
Smallville
Don’t name sci-fi shows? Surely X Files is at least half science fiction, as so many of its episodes deal with aliens.
Poltergeist: The Legacy
Friday the 13th: The Series
The Real Ghostbusters
Kolchack, the Night Stalker
Scooby Doo
Relic Hunter
The Xena & Hecules series
They’re not 
Charmed
If Scooby Doo is accepted, then
Probe works (while the tones are entirely different, in both shows the ‘supernatural’ has an ordinary explanation)
Several kids shows in the ‘deal with’ category :
The Zack Files
So Weird
Strange Days at Blake Hoolsey High (not sure if that’s the right name)
What was that short-lived fox? show about the kids with the website who dealt w/ the paranormal crap?
Special Unit 2 – a show about a Chicago crime squad designed specifically to defeat paranormal types.
Freekylinks?
Eerie Indiana
American Gothic
Haunted
Dead Last
that new show Supernatural
Forever Knight
I think he means just means Scifi shows that have different casts each episode - the aforementioned Twilight Zone, The Outer Limits, Night Visions, Strange Frequency etc.
One of my favorite shows, Millennium, starring Lance Henriksen, would seem to meet your requirements.
How I miss that show!
Going WAAAAAAY back:** UFO**.
There was another Fox show filmed in Vancouver B.C. about a National Enquirer type newspaper that involved that sort of thing. It was called The Chronicle.
Another Fox casualty was The Lone Gunmen, an *X-Files * spinoff.
The Dead Zone - the supernatural adversary isn’t one with a personality, but I think it fits the requirements.
Well, the new Fall TV season is chick full of them:
Supernatural
Ghost Whisperer
Invasion
Triangle
Threshold
Night Stalker (a remake of the old one)
And there have been some relatively new ones already on:
The 4400
Medium
Some others that I’ve watched over the years are:
The Others
Miracles
Tru Calling
Dead Like Me
Wonderfalls
And then I guess it depends on your definition of paranormal. Lost might count, depending on what the outcome of that series is. Fantasy Island, particularly the Malcolm McDowell remake, had definite paranormal elements.
thwartme
Night Stalker.
Some of the scooby-doo series don’t count. Everyone was just a guy with a mask.
Though I do remember that in one series with scrappy in it, they did have real monsters, and the movies all had supernatural stuff.