I don’t really watch television all that much, but somehow I have still managed to see every single episode of certain shows (a lot of them because of DVDs, actually). They are:
The Simpsons
Family Guy (I think)
Monty Python’s Flying Circus
24
Stargate SG-1
Stargate Atlantis (a new show, so this is not much of an achievement)
How 'bout everyone else?
Frasier
Friends
Fawlty Towers
Jeeves and Wooster
Star Treck TNG
Star Treck Voyager
Family Guy (I think)
Futurama (I think)
Only Fools and Horses. :smack:
Buffy the Vampire Slayer
Angel
MAS*H
Hogan’s Heroes
The Rockford Files
Star Trek (TOS)
and of course,
She Spies 
Simpsons
The Simpsons
Futurama
Frasier
Roseanne
Seinfeld
Cheers
Simpsons
Seinfeld
Futurama
Family Guy
Firefly
Stargate: SG1
Stargate: Atlantis
John Doe
Millenium
Magnum: PI
Gilligan’s Island
Star Trek: TOS
24
The Dead Zone
The Shield
MASH
Star Trek: TOS
Babylon 5
Probably a few others, but those are the ones I can identify for sure.
Firefly.
Alas, it was only 14 episodes. 
Twin Peaks
Buffy
Angel
MP’s Flying Circus
BlackAdder
Absolutely Fabulous
Current shows:
Lost
Veronica Mars
Coupling
The Sopranos
Carnivale
Buffy
AFAIK, that’s it for recent shows. It’s likely that I saw every episode of things like The Cosby Show and The Brady Bunch, but I can’t say for sure.
Turn-On
Once a Hero
Star Trek
Star Trek TNG
Monty Python
The West Wing (though that will change soon)
Homicide: Life on the Street
I’ll Fly Away
Lois and Clark
Wings
The Nanny
Friends
Gilligan’s Island
Bewitched
The Brady Bunch
Desperate Housewives
Seinfeld
Sopranos
Curb Your Enthusiasm
Six Feet Under
The Apprentice
Fawlty Towers
Larry Sanders
Twilight Zone
Buffy
Angel
Red Dwarf
Family Guy
Friends (I think)
Blackadder
Futurama
This question gets much easier to answer in the era of shows-released-on-DVD. There are only two shows that I saw every episode of, when originally broadcast (although sometimes tape-or-TIVO-delayed a few days):
My So Called Life
and
24
And I came very close with:
Once and Again
and
Relativity
24 (through season 3)
Buffy
Angel (through season 4; season 5 doesn’t come out until next month)
CSI: Las Vegas (through season 4)
Firefly
The Simpsons (through season 5)
In other words, if it was out on DVD, I’ve seen every episode of it.
Like someone else mentioned, I’ve probably seen every episode of The Brady Bunch, but I’m not positive.
Well, the only one I can think of would be Andy Richtor, but they haven’t released or aired all the episodes so I can’t say I have seen every single one. However, I can come close to saying I have seen most of and possibly all of Futurama, Family Guy, and the “prime” seasons of the Simpsons.
Star Trek TOS
Star Trek TNG
Star Trek Enterprise
American Gothic
Lost
X Files
Firefly
Maybe some others, that’s all that come to mind off the top of my head. Looks like it’s mostly sci-fi type shows for me.