A character that does not appear in every episode, but is in enough of them to affect the storyline on a regular basis. Sometimes called a "semi-regular" character to contrast with the regular characters.
A Living Prop or Spear Carrier who appears repeatedly may become a Recurring Character. If there are so many of these characters any normal episode starts to look like an army, you might have Loads and Loads of Characters.
If they are popular enough to become a regular, they get a Promotion to Opening Titles. For a character who starts out as a regular but becomes recurring over time, see Commuting on a Bus. For the opposite, a character that starts out as a recurring character but eventually due to becoming popular with the audience gets added into the main cast, you have Breakout Character. If they appear in most (or all, in some cases) episodes and get more appearances than even some of the show's regular characters yet continue to be recurring, then they'll wind up being a Fake Guest Star.
No examples — almost every show is going to feature recurring characters in one way or another. (The exceptions would be anthology shows like Black Mirror.)