These are some TV shows where all episodes of them known to exist are available on YouTube (they're all in playlists, making it easier to find the episode you're looking for):
Adult (not suitable for children)
Popetown (10 episodes, presumably in 1 season) - Popetown is a British adult animated sitcom billed by its producers as "Father Ted meets South Park". The series was internationally controversial and wasn't screened by the UK channel that commissioned it: BBC Three. However, Popetown aired in other countries such as New Zealand and even was released on DVD in some places, such as the UK.
The Nutshack (16 episodes, all in 2 seasons) - The Nutshack is an American adult animated TV series created by Ramon Lopez and co-created by Jesse Hernandez. The series ran on Myx TV for 2 seasons, the first in 2007 for 9 episodes and the second in 2011 for 7 episodes. Interestingly, that show's intro is an internet meme. Examples of that meme usually involve that intro.
Anime (for an anime show to be in this list, all episodes of the original show known to exist must be in the playlist and also be dubbed into English)
Kill Me Baby (13 episodes, all in 1 season (those videos aren't there any more, but I'll keep the playlist up for historical purposes and maybe find the episodes again)) - Kill Me Baby is a Japanese four-panel manga series written and illustrated by Kaduho which began serialization in Houbunsha's Manga Time Kirara Carat from July 2008. It follows the school lives of high school girl Yasuna Oribe, along with her friends Sonya, a female assassin, and Agiri Goshiki, a female ninja. An anime adaptation by J.C.Staff lasting for 13 episodes aired in Japan between January 5th 2012 and March 29th 2012 with an original video animation episode being released on October 16th 2013.
Children's
Razzledazzle (20 episodes, all in 1 season) - Razzledazzle is an educational show that aired on the BBC's CBeebies channel and features Razzledazzle, a little orange CGI character with floppy ears and big eyes voiced by Bethen Marlow. I remember watching this show, as well as many other shows, on CBeebies when I was younger.