Of course the series has to have ended already.

Two for me:
* Buffy
* Alias

All of these I have not missed a single episode that I can think of off the top of my head. There's a shit load of 1 season shows like Day Break, Vanished that I have also seen from start to finish as well.

Alias
The OC
Close to Home
Walker Texas Ranger
The District
Crossing Jordan (caught up through re-runs on A&E and watched seasons 3-6 live)
Third Watch
Melrose Place
90210
The Shield (I'm counting this since it's ending in 2008 and I don't intend on missing the final 13 episodes)

Friends
The Pretender (and all of the movies)
Crossing Jordan
Medical Investigation
Conviction
Philly

I'm pretty sure I've seen every episode of The Brady Bunch

Friends
Seinfeld
The Brady Bunch

I'd estimate somewhere around 74

Hmm I don't know if I could remember them all. Off the top of my head:

Shows that have ended:
Farscape
Babylon 5
Buffy
Angel
Firefly
Sopranos
Six Feet Under
Carnivale
Rome
Deadwood
John From Cincinatti
Kindred
Surface
Invasion
Keen Eddie

Shows currently still in production or have not finished airing:
The Wire
Family Guy
American Dad
Desperate Housewives
The Shield
Curb Your Enthusiasm
Journeyman

OK, I don't feel like listing anymore, but I know that list is not complete. It would just take too long to figure it out.

Alias
Angel
Buffy the Vampire Slayer
Dawson's Creek
Felicity
Friends
Will and Grace
Queer as Folk
Sex and the City
Six Feet Under
Roswell
Charmed
Dark Angel
Futurama
I love LUcy
Northern Exposure
The OC
Popular
Twin Peaks
Veronica Mars

Just on DVD I own and have seen the complete series of:

Adventures of Brisco County Jr., The
Airwolf (I don't consider the 4th season to be part of the series)
Arrested Development
Babylon 5
Battlestar Galactica
Clerks
Coupling
Crusade
Firefly
Greg the Bunny
Jack of All Trades
NewsRadio
Nowhere Man
Office, The
Roswell
Sports Night
Star Trek: DS9
Star Trek: The Animated Series
Titus

I've also seen the complete series of Farscape on DVD although I don't own that one. I'm sure there's plenty of other series I've seen every episode of on TV.

Sports Night
The X-Files
Millenium
Deadwood
Six Feet Under
Titus
Arrested Development
Twin Peaks
Seinfeld
Carnivàle
Profit
The Critic
The Loop

Buffy
Angel
Firefly
Seinfeld
Freaks and Geeks
Fresh Prince
Arrested Development
Dead Like Me
Clerks Animated
The Sopranos
Chappelle's Show

Still in production:

Curb
House
Reaper
Smallville
Weeds
Pushing Daisies
The Office (US)
Entourage

Oh hell no. I don't want to depress myself.

I'll stick with shows that have at least 50 episodes. Listing 1 or 2 season shows would make this way too long.

Still On:
Aqua Teen Hunger Force
Family Guy
House
Lost
Prison Break
Robot Chicken
Simpsons
South Park

Off air:
Earth: Final Conflict
Futurama
Saved by the Bell (yeah, yeah)
Sealab 2021
Seinfeld
Star Trek OS
Star Trek TNG
X Files

Plus a bunch of cartoons as a kid.

Nip/Tuck (thus far)
The Shield (thus far)
Star Trek
Star Trek TNG
Rescue Me (thus far)
The Office (american version) (thus far)
30 Rock (thus far)
Scrubs (thus far)
Supernatural (thus far)
Firefly
Battlestar Galactica (original)
Battlestar Galactica (remake) (thus far)
Significant Others

That's my answer too.

I can't say I have actually ever counted. Once I've watched a show at least a year or two (Grey's Anatomy and Family Guy being the two big exceptions), I stick with it until the end.

Friends
Buffy
Firefly
Freaks and Geeks
Veronica Mars
Alias
Sex and the City
The Sopranos
DS9
Charmed

I'm sure there are a few dozen shows of which I've seen every episode.

Just a few off the top of my head.
M*A*S*H (of course)
Batman
The Sopranos
NYPD Blue - I'm pretty sure I saw every episode in its first airing.
The Brady Bunch
Veronica Mars
Seinfeld
Friends

If we're limiting it to series that are done(and lasted more than 2 weeks):

Buffy
Angel
Friends
Firefly
Undeclared
Coupling(UK)
The Office(UK)
Arrested Development
The O.C.
The Class
Da Ali G Show

I've only seen every episode of Freaks & Geeks , amazing series. When I purchased the limited Yearbook edition, I devoured every episode of the show in 2 days and read through every page of the yearbook, then went back and listened to most of the commentaries on the first few discs.

I never have that kind of time available, but for Freaks & Geeks, I made time

Friends
The X-Files
Millennium
Freaks & Geeks
My So-Called Life
Futurama
Northern Exposure
Three's Company
The Office (UK)
Arrested Development
Firefly
Six Feet Under
Oz
Twin Peaks

Alias
Arrested Development
Angel
Buffy the Vampire Slayer
Friends
Will and Grace
Queer as Folk (US and UK)
Absolutely Fabulous
Mr. Show
Cheers
SOAP
The Young Ones
Moonlighting
Sex and the City
Six Feet Under
Millennium
X-Files
Seinfeld
NewsRadio
Kids in the Hall
Monty Python's Flying Circus
The Sopranos
Futurama
Undeclared
Greg the Bunny
Freaks and Geeks
Firefly
Twin Peaks
Veronica Mars
Friends

... oh yeah - and Viva Laughlin and Emily's Reasons Why Not.

Buffy
Angel
Arrested Development
Firefly
Six Feet Under
Office (UK)
Veronica Mars

Still Airing:
Prison Break
Heroes
The Shield
Rescue Me
Nip / Tuck
Smallville
The Office
Desperate Housewives

I can't say I've seen every episode of a series, although Duck Tales and Tale Spin come pretty close.

Firefly
The Office
Extras
Freaks and Geeks
West Wing
Brisco county Jr.
Arrested Development
Spaced
Mr. Show
Sopranos
Rome
Deadwood

Top of head..

X-Files
NYPD Blue
Sopranos
Dream On
Gilligans Island
The Critic
Dancing with the Stars
CSI
Friends