If you're talking something that beginners should learn and veterans should know, I'd have to say "Stand By Me" by Ben E. King. That is classic Motown and can be used in many songs like Please Mr. Postman and other oldies.
It is an instantly recognizable progression that stands on its own. May be a bit below your skill level, however.
Great example. Yeah it may be a basic riff, but it speaks volumes about how you don't need a million notes to make a memorable bass line. I believe I know this one, but will work on it regardless.
This is one all bass players should know.