In no particular order:

Fox Mulder - X-Files
Tony Soprano - The Sopranos
Jean-Luc Picard - ST:TNG
Homer Simpsons - The Simpsons
Kramer - Seinfeld
Tyrion Lannister - Game of Thrones
Larry David - Curb Your Enthusiasm (with a sideways shout out to George Costanza)
Don Draper - Mad Men
Larry Sanders - The Larry Sanders Show
Jimmy McNulty - The Wire

Kerr Avon (Blake's 7)
Gene Hunt (U.K. Life on Mars and Ashes to Ashes)
Stringfellow Hawke (Airwolf)
David Brent (U.K. The Office)
Emma Peel (The Avengers)
Londo Mollari (Babylon 5)
The Doctor (Doctor Who)
Dale Cooper (Twin Peaks)
Wesley Wyndam-Pryce (Angel)
Dr. Gregory House (House)

Saul Goodman - Breaking Bad
Kenneth - 30 Rock
Carrie Matheson - Homeland
Larry Sanders - The Larry Sanders Show
Ron Swanson - Parks & Recreation
Ari Gold - Entourage
Gus Fring - Breaking Bad
Jack Donaghy - 30 Rock
Jeff Winger - Community
Phil Dunphy - Modern Family

I missed this in August.

That was my 2003 list.

I know the following still make the cut:

Jimmy James - Newsradio
Vic Mackey - The Shield
Lorelai Gilmore - Gilmore Girls (though really that last season hurt her so badly)

That leaves 7 spots up for grabs.

Ron Swanson - Parks and Rec - makes the list for OBVIOUS reasons - goodbye Sexual Harrassment Panda
Abed Nadir - Community - ditto - goodbye Benson
Raylan Givens - Justified - to keep the group in order and as a love interest for the women for comedy sake if this is a collection of people I'm watching - he boots out Wesley Wyndam-Price
Kimber Henry - Nip/Tuck - my gosh how much fun this would be - goodbye to Daria
Veronica Mars - Veronica Mars - goodbye Natalie Hurley
Data - Star Trek: TNG - goodbye Tobias Beecher
Tobias Fünke -Arrested Development - goodbye to David Puddy

Yes, I like that quite a bit.

ETA: This is a runners up list, of characters I didn't choose because they were the second best on their shows of what have you:

Annie Edison - Community
April Ludgate - Parks and Rec
Cindy "Mac" Mackenzie - Veronica Mars
Lisa Miller - Newsradio
George-Michael Bluth - Arrested Development
Worf - TNG
Christian Troy - Nip/Tuck
Holland "Dutch" Wagenbach - The Shield
Rory Gilmore - Gilmore Girls
Boyd Crowder - Justified

That's not my second ten (at least not partly) but it's the second string on the shows I have identified. Number 11 on my list would be Michael Westen from Burn Notice.

1. Raylan Givens - Justified
2. Malcolm Reynolds - Firefly
3. Starbuck - BSG
4. Faith - Buffy the Vampire Slayer
5. Titus Pullo - Rome
6. Veronica Mars - Veronica Mars
7. Dr. Walter Bishop - Fringe
8. Winifred Burkle - Angel
9. Ron Swanson - Parks & Rec
10. Mr. Gold - Once Upon a Time

Jack Tripper - Three's Company
Roger Smith - American Dad
Alex P. Keaton - Family Ties
Dale Cooper - Twin Peaks
Bender Rodriguez - Futurama
Sterling Archer - Archer
Tim Canterbury - The Office (UK)
Al Swearengen - Deadwood
Gob Bluth - Arrested Development
Chandler Bing - Friends

Jeff Murdoch (Coupling)
Brisco County, Jr. (The Adventures of Brisco County, Jr.)
Londo/G'Kar (Babylon 5)
Veronica Mars (Veronica Mars)
Kaylee Frye (Firefly)
Gob Bluth (Arrested Development)
Jack Bauer (24)
Shawn Spencer (Psych)
Tom Servo (MST3K)
Ken Titus (Titus)