Well, no.
In ANH, he serves as the storyteller, bringing us through the action of the film (and interpreting for R2-D2).

In ESB, he might be mostly comical, but he serves a key role in building the tension on Cloud City. Even if it's a small role, he serves the story in some way.

In RotJ, he's the ambassador to the Ewoks, who are integral in the Rebellion's success on Endor.

However.... in the prequels, C-3P0 does nothing for the story. Nothing at all. He makes a stupid naked joke in TPM, he bumbles around and has some stupid puns in AotC, and he makes some pointless remarks in RotS.