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 character that starts out as a recurring character but eventually joins the main cast is a case of them getting a Promotion to Opening Titles. If this promotion happens mainly because of fan popularity, then you've got yourself a Breakout Character. Conversely, for a character who starts out as a regular but becomes recurring over time, see Commuting on a Bus. Finally, if they appear in so many episodes that they get more appearances than even some of the show's regular characters, yet the credits insist on only giving them guest billing, then they're a Fake Guest Star.
No examples, please. Almost every show that isn't a One-Episode Wonder is going to feature recurring characters in one way or another. The only notable exception is the Genre Anthology, and even then, some anthologies can have recurring characters if its stories are within a shared universe (e.g. American Horror Story or Infinity Train).