Roxy Music is a really good call. Song For Europe has a gorgeous melody I think.

Other songs I can think of with great melodies:

David Bowie - Five Years
The Beach Boys - Disney Girls
Big Star - Ballad of El Goodo
The Beatles - We Can Work it Out
The Bangles - Going Down to Liverpool
The Band - The Weight

(Something about melody and the letter B, evidently)

Whoa, there are so many favourites

Angelo Badalamenti's Twin Peaks theme
The Synth-Intro to Robert Palmer's "You are in my System"
Joy Division - Disorder
Chet Baker - But not for me
Combichrist - Today we are all demons
OMD - 2nd Thought
MBV - Never Say Goodbye
The Diamond Sea
Wish Fulfillment
Wild Flower Soul
Pink Steam

etc...

van morrison - everyone
rolling stones - she's a rainbow
velvet underground - sunday morning
tom tom club - genius of love
the vaselines - son of a gun
blondie - fade away and radiate
M83 - graveyard girl

that's my mom's ringtone.

----

omd - if you leave
joni mitchell - all i want
crystal castles - untrust us
broadcast - america's boy

haha my mom's ringtone is paint it black

fuck yeah, classic melody.

Thought of some more...60s, anyone?

The Zombies: She's Not There
Strawberry Alarm Clock: Incense and Peppermints
The Doors: Light My Fire

I kind of hear a similar vibe sometimes with sunday morning and son of a gun and even mollys lips.

But hell yes to those two.

Captain Beefheart- Grown so Ugly

I agree with everything there. Also, Vaselines - Lovecraft.

Most notably "When The Sun Shines Down On Me", "Story Of An Artist", and "Don't Let The Sun Go Down"..