Elton John: “Love Lies Bleeding”, “Funeral for a Friend”, just about anything of his from the seventies.
Billy Joel: “The Piano Man”, “Captian Jack”, “Billy the Kid”, I could go on and on but they are the first few that came to mind.
Someone else mentioned Led Zeppelin. I know it’s a cliche, but “Stairway to Heaven” (there’s a reason it’s become a cliche). Also “When the Levee Breaks”.
Neil Young: (I’m listening to his greatest hits CD as I’m typing this so I’ve got a list at hand which is very hard to narrow down.) “Down by the River”, “Cowgirl in the Sand”, “Cinnamon Girl”, “Helpless”, “After the Gold Rush”, “Only Love can Break Your Heart”, “Southern Man”, “Ohio”, “The Needle and the Damage Done”, “Old Man”, “Heart of Gold”, “Comes a Time”, “Hey Hey My My”, “Rockin in the Free World”
Someone made a brief mention of The Beatles and The Rolling Stones. It’s hard to know where to even start with them. Check out as much of their stuff as you can.
Just about anything from the Stones is worthwhile (although I’m not really familiar with their really recent stuff).
I know you don’t want to hear about albums but with the Beatles it’s hard not to talk in terms of albums, at least with their later stuff. They were meant to be listened to as a whole. You may want to try it out just to understand.
I love anything by the Beatles but the best stuff, at least for me, is anything from “Help!” (1965) and later. In particular “Sgt. Pepper’s Lonely Hearts Club Band”, “Magical Mystery Tour”, “The Beatles [White Album]” (probably my favorite), " Abbey Road", “Hey Jude”, and “Let It Be”. If you’re really dead set against albums, see if you can sample some clips and just pick the singles you really like. To someone from my generation it almost seems blasphemous to pull a Beatles song out of it’s context, but I understand that that’s because of the times I grew up in and you may feel differently.
For any of the artists mentioned in this thread, sample as many clips as you can because there’re sure to be things you’ll like that no one will think to mention.