I came across this post because I was looking for some new songwriters to listen to myself, but I joined the site to reply because Elvis Costello, the Beatles, and the Beach Boys are among my favorite melody writers. (Buddy Holly wrote some great stuff, too, but he was usually working within a pretty conventional 12-bar blues format.)
I agree with several of the other responses: in addition to Elvis, Lennon/McCartney, and Brian Wilson, my top-ten list of great melody writers would definitely include Ray Davies (particularly on Village Green Preservation Society), Billy Joel (even though his lyrics are usually terrible and half of his songs are pretty half-assed musically), Leonard Bernstein (West Side Story), and Richard Rodgers (Sound of Music, etc.). Along the same lines, I think that Kate Bush is a pretty good recommendation, too, although I wouldn't quite put her in the same league as those other guys.
Other recommendations mystify me: for instance, I *love* Robbie Robertson, Leonard Cohen, and Stevie Wonder, but none of them is a particularly notable melody writer -- at least not in the sense that the other people you mention are, in terms of melodic and harmonic complexity. (Stevie Wonder is a musical genius, but his imagination is more contrapuntal, rhythmic, and textural than straightforwardly melodic.)
Okay, so, if I'm working from a list that includes Elvis, Lennon/McCartney, Brian Wilson, Ray Davies, Billy Joel, Bernstein and Rodgers, then, to me, there are two notable omissions: David Bowie (in the '70s, at least; by his own admission, he pretty much stopped trying to write memorable melodies in the late '80s) and Burt Bacharach (don't let the cheesy arrangements fool you!).
Not quite in that top tier but close behind, I'd also recommend XTC, Aimee Mann (particularly on Bachelor No. 2), Michael Penn (particularly his first album), and, a kind of oddball pick, I know, Thomas Dolby (particularly Golden Age of Wireless). I also think Joe Jackson at his best is as good as anybody, but unfortunately, he was rarely at his best.
Finally, if you like Elvis, the Beach Boys, and the Beatles, you might also dig my stuff, since I was heavily influenced by all three of them: hopefulmonsters.org/beta/majordealinlife.html.
