I agree with most of Paul's answer.
Don't do it. Declining fellowships is one thing, maybe still don't do that either. But telling grad school admissions you rejected, or job offers you rejected, or invitations to the prom you rejected (!?!) is considerably off-putting, and probably does more to make people think they'd be happier not having you around, no matter your other purported virtues.
BUT, a another reason for not including is that it is a waste of space and looks like a filler (i.e., you have nothing better to write or if you have do have better things to write, this dilutes them).
Although academic CV's are notoriously long (and defined as Latin for “course of (one’s) life" in a dictionary, including trivial things gives the appearance you either have nothing better to say (e.g., you are an early-career persons) or are padding your CV with details that do not matter. Thus, you're taking the course of one's life too literally or in too fine of detail.
However, I have seen people tactfully list declining fellowship and list this under as an honor or award similar to NSF's Honorable Mentions (e.g., offered NSF fellowship X and DOE fellowship Y and selected the DOE fellowship Y because... or NSF GRFP Honorable Mention).