Cartoon Network (see also Toonami, Fridays, Adult Swim, Miguzi, SVES, Action Fridays, Mondays, and DC Nation)
(launched in 1992)
IMDb; official website; TV Tropes; Wikia; Wikipedia

While the channel has aired countless old shows that originally aired on other networks, I'm only going to list shows that originally aired on Cartoon Network. Well, American shows; but I'll also list some shows from other countries if Cartoon Network was the first American channel to air them.
For shows aired in the channel's Adult Swim block, see Adult Swim.
(Note: I lost access to Cartoon Network in June 2011, so there's a lot I haven't been able to see since then, and some things I may have seen on DVD or other channels/online.)

1990s
Space Ghost Coast to Coast (4/15/1994 - 7/22/2001; s7e3-s9 aired on Adult Swim; s10-11 released on GapTap)
What a Cartoon! (2/20/1995 - 11/28/1997)
Cartoon Planet (9/10/1995 - 2/4/1998; premiered on TBS)
Dexter's Laboratory (4/28/1996 - 11/20/2003)
Johnny Bravo (7/14/1997 - 8/27/2004)
Cow & Chicken (7/15/1997 - 7/24/1999)
The Powerpuff Girls (11/18/1998 - 3/25/2005)
Ed, Edd n Eddy (1/4/1999 - 11/8/2009)
Ego Trip (12/10/1999; special)

other: CN Groovies / CN Shorties

2000s
Brak Presents the Brak Show Starring Brak (2/20/2000; special)
Toonami: The Intruder (9/18/2000 - 11/24/2000; microseries)
Time Squad (6/8/2001 - 11/26/2003)
Samurai Jack (8/10/2001 - 9/25/2004; s5 on Adult Swim in 2017)
Night of the Living Doo (10/31/2001; special)
Justice League (11/17/2001 - 5/29/2004)
Codename: Kids Next Door (12/6/2002 - 11/23/2007)
The Grim Adventures of Billy & Mandy (6/13/2003 - 10/12/2008)
Totally Spies! (7/7/2003 - 6/1/2010; s1 aired on ABC Family; spawned a movie in 2009 and a 6th season in 2013; originally on TF1 in France and Teletoon in Canada)
Teen Titans (7/19/2003 - 9/15/2006)
Duck Dodgers (8/23/2003 - 11/11/2005)
IGPX (9/15-19/2003; microseries)
Star Wars: Clone Wars (11/7/2003 - 3/25/2005)
'Twas the Fight Before Christmas (12/12/2003; special)
Code Lyoko (4/19/2004 - 11/17/2007; originally aired on France 3)
Megas XLR (5/1/2004 - 1/15/2005)
Justice League Unlimited (7/31/2004 - 5/13/2006)
Foster's Home for Imaginary Friends (8/13/2004 - 5/3/2009)
Hi Hi Puffy AmiYumi (11/19/2004 - 6/27/2006)
Krypto the Superdog (3/25/2005 - 12/15/2006)
The Life and Times of Juniper Lee (5/30/2005 - 4/9/2007)
Ben 10 (12/27/2005 - 4/15/2008)
Operation: ZERO (8/11/2006; TV movie)
Teen Titans: Trouble in Tokyo (9/15/2006; TV movie)
Ellen's Acres (9/29/2006 - 2/5/2007?)
Good Wilt Hunting (11/23/2006; special)
Re-animated (12/8/2006; TV movie)
Ben 10: Race Against Time (11/21/2007; TV movie)
Transformers Animated (12/26/2007 - 5/23/2009)
Operation: INTERVIEWS (1/21/2008; special)
Ben 10: Alien Force (4/18/2008 - 3/26/2010)
Total Drama Island (6/5/2008 - 12/18/2008; originally on Teletoon, in Canada)
The Secret Saturdays (10/3/2008 - 1/30/2010)
Star Wars: The Clone Wars (10/3/2008 - 3/2/2013; s6 on Netflix, s7 on Disney+)
Batman: The Brave and the Bold (11/14/2008 - 11/18/2011)
Destination Imagination (11/27/2008; TV movie)
Scooby-Doo! The Mystery Begins (9/13/2009; TV movie)
The Super Hero Squad Show (9/14/2009 - 10/14/2011)
Ben 10: Alien Swarm (11/25/2009; TV movie)

2010s
Adventure Time (4/5/2010 - 9/3/2018)
Ben 10: Ultimate Alien (4/23/2010 - 3/31/2012)
Generator Rex (4/23/2010 - 1/3/2013)
Mad (9/6/2010 - 12/2/2013)
Regular Show (9/6/2010 - 1/16/2017)
Sym-Bionic Titan (9/17/2010 - 4/9/2011)
Firebreather (11/24/2010; TV movie)
Young Justice (11/26/2010 - 3/16/2013; s3 on DC Universe)
The Amazing World of Gumball (5/3/2011 - 6/24/2019)
DC Nation shorts (11/11/2011 - 8/2/14)
Dreamworks Dragons (8/7/2012 - 3/5/2014; season 3 onward on Netflix)
Over the Garden Wall (11/3-7/2014; miniseries)
DC Super Hero Girls: Super Hero High (4/30/2016; previously aired on Boomerang)

stuff I want to see
Ben 10: Omniverse
Beware the Batman
Cloudy with a Chance of Meatballs
Craig of the Creek
DC Super Hero Girls
Green Lantern: The Animated Series
Infinity Train
Justice League Action
Level Up
Mighty Magiswords
The Powerpuff Girls (reboot)
Steven Universe
Teen Titans Go!
ThunderCats (reboot)