The WB (Warner Bros.; see also Kids' WB and Warner Bros.)
(launched in 1995; merged with UPN in 2006 to form The CW)
IMDb; TV Tropes; Wikipedia

1990s
Animaniacs (9/9/1995 - 11/14/1998; s1-2 aired on FOX)
Freakazoid! (9/9/1995 - 6/1/1997)
Pinky and the Brain (9/9/1995 - 11/14/1998)
Superman (9/6/1996 - 2/12/2000)
Buffy the Vampire Slayer (3/10/1997 - 5/22/2001; s6-7 aired on UPN)
The New Batman Adventures (9/13/1997 - 1/16/1999)
Men in Black: The Series (10/11/1997 - 6/30/2001)
Dawson's Creek (1/20/1998 - 5/14/2003; I only saw s1)
Invasion America (6/8/1998 - 7/7/1998)
Batman Beyond (1/10/1999 - 12/18/2001)
Detention (9/11/1999 - 3/25/2000)
Mission Hill (9/24/1999 - 7/16/2000; 6 more episodes aired on Adult Swim in 2002)
Angel (10/5/1999 - 5/19/2004)
Roswell (10/6/1999 - 5/21/2001; s3 aired on UPN)

2000s
Baby Blues (7/28/2000 - 8/24/2000; 5 more episodes aired on Adult Swim in 2002)
Jackie Chan Adventures (9/9/2000 - 7/8/2005)
Sabrina the Teenage Witch (9/22/2000 - 4/24/2003; s1-4 aired on ABC)
Static Shock (9/23/2000 - 5/22/2004)
Gilmore Girls (10/5/2000 - 5/9/2006; s7 aired on The CW)
X-Men: Evolution (11/4/2000 - 10/25/2003)
The Zeta Project (1/27/2001 - 8/10/2002)
The Oblongs (4/1/2001 - 5/20/2001; 5 more episodes aired on Adult Swim in 2002)
Cubix: Robots for Everyone (8/11/2001 - 4/26/2003; aired on KBS in South Korea)
Dead Last (8/14/2001 - 9/25/2001; 7 episodes never aired)
The Nightmare Room (8/31/2001 - 3/16/2002)
Reba (10/5/2001 - 5/5/2006; s6 aired on The CW)
Smallville (10/16/2001 - 5/11/2006; s6-10 aired on The CW)
Glory Days (1/16/2002 - 3/25/2002)
Mucha Lucha (8/17/2002 - 2/26/2005; I didn't see much of this)
Family Affair (9/12/2002 - 3/13/2002; 2 episodes never aired)
Ozzy & Drix (9/14/2002 - 7/5/2004)
Do Over (9/19/2002 - 12/5/2002; 4 episodes never aired)
What I Like About You (9/20/2002 - 3/24/2006)
Birds of Prey (10/9/2002 - 2/19/2003)
Run of the House (9/11/2003 - 5/7/2004; 3 episodes never aired)
Tarzan (10/5/2003 - 11/23/2003)
Xiaolin Showdown (11/1/2003 - 5/13/2006)
Astro Boy (1/17/2004 - 3/30/2004; originally aired on Fuji TV in Japan; 21 episodes never aired on the WB)
Summerland (6/1/2004 - 7/18/2005)
The Batman (9/11/2004 - 5/13/2006; s4-5 aired on The CW)
Samantha: An American Girl Holiday (11/23/2004; TV movie)
Supernatural (9/13/2005 - 5/4/2006; s2-15 aired on The CW)
Loonatics Unleashed (9/17/2005 - 5/13/2006; s2 aired on The CW, but I don't think I even saw all of s1)
Viewtiful Joe (11/5/2005 - 5/20/2006; originally aired on TV Tokyo in Japan; s2 never aired in the U.S.)
Felicity: An American Girl Adventure (11/29/2005; TV movie)

stuff I want to see
Charmed
Felicity
The Legend of Calamity Jane
The Mummy (I saw a bit of this, but I wouldn't mind seeing more)
Savannah