I’m limiting myself to fictional shows as opposed to interview shows or shows dependent upon the news.
The Wire
The West Wing
Angel
The Wonder Years
Seinfeld
Lost
X-Files
Freaks and Geeks
House
MI-5 (Seriously slept on.)
Sad that no one has mentioned The Larry Sanders Show yet; they have *got *to get those DVDs sorted out.
Aside from that, the only two shows that I would feel obligated to mention are The Simpsons and The Wire. After those three, there are maybe 40 or 50 shows that rotate in and out of my Greatest 10 list.
The West Wing
Simpsons
The Wire
Weeds
Futurama
Cheers
Seinfeld
Roseanne
NOVA
The Daily Show
Star Trek
Saturday Night Live
Meet the Press
The Tonight Show
CBS Evening News
Hill Street Blues
Doctor Who
The Real World (Why? Because it was the first “reality” show)
Sesame Street
NOVA/Frontline
Otherwise known as the Bryan Fuller rule? (Not just Pushing Daisies, but Dead Like Me, and Wonderfalls)
Not ten, but more votes for
-Buffy
-Lost *
-Six Feet Under
-The Wire
-Burn Notice *
-Dexter *
- I’m a little reluctant to list these shows, since they’re still in progress, and have a shot at screwing it all up.
And I have great hopes for two shows that are disqualified by only entering their second season:
-Fringe
-Dollhouse
This is what I intended everybody to do, but I neglected so so specify in the OP. Clearly I am a fool of a Took. 
That’s cool. I mean, I was pretending that the third season of Star Trek and at least half of the Simpsons were a lot better than everybody knows they are.
In random order except for #1:
The Wire
I Love Lucy
Hill Street Blues
Dick Van Dyke Show
St. Elsewhere
Seinfeld
The Tonight Show with Johnny Carson
Mary Tyler Moore Show
Saturday Night Live
The Amazing Race
Can I knock the Beverly Hillbillies off my list & put the UK version of Whose Line is it Anyway on. Just been watching a couple of episodes on You tube & laughed till I cried.
I can’t list 10. Joss Whedon’s only made 4! 
The Wire
Arrested Development
Twin Peaks
The Bob Newhart Show (the first one)
The Mary Tyler Moore Show
Shameless
MASH
Rome
American Experience
The Duchess of Duke Street
NOVA
I don’t know if these are the ten GREATEST, but they’re definitely my favorites:
- Curb Your Enthusiasm
- Felicity
- Seinfeld
- So You Think You Can Dance
- The Office (US version)
- Sex and the City
- Alias
- Strangers with Candy
- America’s Test Kitchen
- The Daily Show
[ol]
[li]Twin Peaks[/li][li]I, Claudius[/li][li]Lonesome Dove[/li][li]Connections[/li][li]Fernwood Tonight[/li][li]Monty Python[/li][li]Fawlty Towers[/li][li]Blackadder[/li][li]60 Minutes[/li][li]Lost[/li][/ol]
and
MASH
I Love Lucy
All in the Family
West Wing
30 Rock
Nearly all of my Top Ten have appeared in one person’s post or another’s, but I cannot fully support any list that doesn’t contain Cowboy Bebop.
The Simpsons
Saturday Night Live
Law & Order
NewsRadio
Bonanza
The Twilight Zone (the original)
The Tonight Show with Johnny Carson
The Jack Benny Program
The Ed Sullivan Show
Hill Street Blues
Dream On (HBO)
Married With Children
Roseanne
Northern Exposure
ER
NYPD Blue
Mad Men
Days and Nights of Molly Dodd
Carnivale (HBO)
Upstairs Downstairs
Honorable mention: WKRP in Cincinnati, MASH, Lexx, Andromeda, Lost, The Red Green Show 
There. Give me complete box sets of all these shows and I’ll have enough good stuff to watch until I die. Not a supermodel, fat person, survivor, great racer, yakking housewife, or Tori Spelling among the above, please note.
Actually had this but then remembered it was only one season.
Don’t know about “Greatest” but I’ve enjoyed:
The Sopranos
The Simpsons
Seinfeld
The Wire
Northern Exposure
Buffy
Cheers
NYPD Blue
Frasier
(While I’m sure they’re great, and I remember watching them as a kid, I’m a little too young for stuff like All In The Family, MASH, Mary Tyler Moore, Johnny Carson etc. to have been “favorites” of mine (never mind older shows like The Honeymooners or I Love Lucy) so I don’t think I can honestly put them in perspective.)
1 - The Wire
2 - Rome
3 - MASH
4 - Doctor Who (which is both one of the greatest and the worst shows ever, depending on which serial you watch)
5 - The West Wing
6 - Babylon 5
7 - Farscape
8- Dexter
9 - The Sopranos
10 - Battlestar Galactica
10 - One of the Star Treks (TOS or TNG)
(This list should really be comprised only of the first 5 shows. Babylon 5 had great writing but poor production values it didn’t always know how to work around and variable acting. Farscape I loved but also had a huge share of problems. The rest I really enjoyed but didn’t really find great. I really, really wish this thread’s rules would allow me to put I, Claudius in there.)
Define “greatest”.
My personal favorites would have to include Cinemax’s weekend lineup, but if we go with shows that I view (heh) as most influential:
- Tonight Show (the definitive talk show)
- The Lucy Show (sitcom)
- Star Trek ([del]religious[/del] SF )
- Twilight Zone (anthology SF with good writing)
- Simpsons (weekly animation)
- Babylon 5 (epic serial)
- Real World (start of the reality TV madness)
- As The World Turns/General Hospital (soap - tie)
- Newhart (if only for the ending of the “Inn in Vermont” series)
I thought 26 episodes meant 2 TV seasons in Japan. “Jupiter Jazz” parts 1 and 2 (eps 12 and 13) sure had the feeling of a season closer.