Nickelodeon (see also Nicktoons, TeenNick, Nick Jr., SNICK, and Nickelodeon Movies)
(launched in 1979)
IMDb; official website; TV Tropes; Wikia; Wikipedia

stuff I've seen
Clarissa Explains It All (3/23/1991 - 10/1/1994; I didn't have a chance to see much of this)
Rocko's Modern Life (9/19/1993 - 11/24/1996; I didn't see much of this)
The Secret World of Alex Mack (10/8/1994 - 1/15/1998)
Figure It Out (7/7/1997 - 12/12/1999; I didn't see a lot of this)
The Journey of Allen Strange (11/8/1997 - 4/23/2000; I don't recall how much of this I saw)
SpongeBob SquarePants (5/1/1999 - present; I haven't seen a lot of this)
Dora the Explorer (6/12/1999 - 8/9/2019; I've seen very little of this)
The Amanda Show (10/16/1999 - 9/21/2002; I didn't see much of this)
Caitlin's Way (3/11/2000 - 4/28/2002)
The Fairly OddParents (3/30/2001 - 7/26/2017; I didn't see a lot of this)
Invader Zim (3/30/2001 - 12/10/2002; s2 aired on Nicktoons in 2006)
My Life as a Teenage Robot (8/1/2003 - 9/9/2005; s3 aired on Nicktoons)
Danny Phantom (4/3/2004 - 8/24/2007)
LazyTown (8/16/2004 - 10/15/2007; two more seasons aired in 2013-2014, which I didn't get to see)
Ned's Declassified School Survival Guide (9/12/2004 - 6/8/2007)
Avatar: The Last Airbender (2/21/2005 - 7/19/2008)
Wonder Pets! (3/3/2006 - 7/20/2013; I probably saw two seasons at most)
Shuriken School (8/20/2006 - 12/22/2007; originally on France 3; I'm not sure when it aired in the US)
El Tigre: The Adventures of Manny Rivera (2/19/2007 - 9/13/2008; I'm not sure how much of this I saw)
iCarly (9/8/2007 - 11/23/2012; I didn't get to see all of this)
Roxy Hunter and the Mystery of the Moody Ghost (10/30/2007; TV movie)
Roxy Hunter and the Secret of the Shaman (2/1/2008; TV movie)
Ni Hao, Kai-Lan (2/7/2008 - 8/21/2011; I've seen very little of this)
Roxy Hunter and the Myth of the Mermaid (7/13/2008; TV movie)
The Troop (9/12/2009 - 8/6/2011; s2.5 aired on Nicktoons; I didn't get to see any of season 2)
The Boy Who Cried Werewolf (10/23/2010; TV movie)
Grow Up, Timmy Turner! (7/9/2011; TV movie)
The Legend of Korra (4/14/2012 - 7/25/2014; s3.5 - 4 released on Nick.com)
A Fairly Odd Christmas (11/29/2012; TV movie)
Liar, Liar, Vampire (10/12/2015; TV movie)
Tiny Christmas (12/2/2017; TV movie)

stuff I want to see
100 Things to Do Before High School (I saw the pilot special)
The Adventures of Pete & Pete
Are You Afraid of the Dark?
Deadtime Stories
Escape from Mr. Lemoncello's Library (TV movie)
Kung Fu Panda: Legends of Awesomeness
Legends of the Hidden Temple (TV movie)
Lost in the West (miniseries)
Monsters vs. Aliens
The Other Kingdom
Sam & Cat
School of Rock
Space Cases
maybe some other stuff