"Late in the Evening" (Paul Simon)

I'm an unequivocal fan of Paul Simon.  He's simply America's poet laureate of modern popular music (alongside Bob Dylan).  From the days when he was writing tunes for himself and Art Garfunkel to his newest solo stuff today, the man has always had a knack for crafting words and melodies that resonate deeply and universally.
(To hell with critics who've picked apart his lyrics over the years or derided him for dipping into the well of world music for inspiration.  Let's see them compose anything half as good as what's on Graceland, and then we'll talk.)
When I was a little kid, my favorite Simon song—apart from the nursery rhyming "50 Ways to Leave Your Lover"—was "Late in the Evening" from the soundtrack for the film One Trick Pony (1980).  
What grabbed me about this particular song?  
First of all, secret-rhythm-weapon Steve Gadd's superlative drumming sets the stage for the track's sweltering Latin funk, which seduces every molecule from your waist down to move.  
Secondly, there's pure joy and celebration in every note of that melody, especially when the brass section arrives.  But it really was Simon's lyrics that did it for me: that image of a young kid lying on his bed, hearing music seeping through the wall from the radio in the next room—it was exactly how I experienced this song for the first time (that is, blasting from the radio in the living room while my mom was doing housework and dancing).  
And what cinched it was that vivid description of him walking down the street, watching guys shooting pool, hearing a cappella groups harmonizing, and seeing girls hanging out on their front stoops.  Even if that distinctly post-WWII New York tableau wasn't in my frame of reference, Simon instantly transported me to that exact place and time.  
Some novelists can't even do that in 300 pages, and he does it in four lines.

"50 Ways to Leave Your Lover" (Paul Simon)

"50 Ways to Leave Your Lover" was the last song that Paul Simon wrote for his 1975 album Still Crazy After All These Years.  Word has it that he considers it kind of a nonsense, throwaway song.  Yet I think it's one of the best things he's ever recorded.
The most clever thing about the song is that the chorus—with its plan/Stan, coy/Roy, bus/Gus nursery school rhyming—isn't the real hook of the song; it's session drummer Steve Gadd's marching pattern on his snare against the time-keeping hi-hat/tambourine and syncopated kick drum.  That funky drum pattern was what always captured my ear as a kid every time the song came on the radio, often prompting me to go marching around our living room.
The icing on the cake is Simon's intricate chord changes in the verse.  The melody skirts the line between the melancholy of an Eastern European folk tune and the soulful, blue melodicism of cool jazz.  In fact, the chord changes remind me a bit of John Lewis's composition "Django"—an homage to the late Gypsy jazz guitarist Django Reinhardt—as first recorded by the Modern Jazz Quartet.
Lyrically, "50 Ways..." is a snapshot of a man who's having an affair.  He's discussing ideas with his girlfriend—who almost takes on a kind of psychiatrist/analyst role to Simon's patient—about how to ditch his other lover.  
Only in recent years did I really get to thinking about the structure of the song—the weighty, emotional subject matter of the verses juxtaposed with the kiddie rhyming in the chorus.  It seems to suggest that, here are two adults, engaged in very adult matters, who aren't really thinking things through.  They're feigning a clinical and logical approach to solving the "problem."  However, they're really acting like little children, having their fun without really considering the consequences.  
Pretty smart on Simon's part.