This is a repost. I think it wasn't properly clear in the last post. I'm not asking for theme songs, I'm asking for songs sung by sitcom characters that stuck with you. Like, Robin Daggers singing "P.S. I love you", or Phoebe with "Smelly Cat", or Raj and Howard and "Thor and Dr Jones", or the entire gang of New Girl with "Nick Miller, Nick Miller, from the streets of Chicago".
There are a few good examples, Thor and Dr Jones, Smelly Cat, Nick Miller Nick Miller from the streets of Chicago.