"Sweet Jane" (The Velvet Underground)

"Accessible" isn't a word that one uses when talking about The Velvet Underground.  Lou Reed & Co. never aimed for the mainstream.  Gutters, alleyways, and anywhere where the light was dim—that was more their territory.
However, after years of not selling any records, the band made an attempt at a pop album called Loaded (1970).  On it, is the track "Sweet Jane," perhaps Reed's most effervescent, accessible composition of all time.  Unlike a lot of songs in the band's catalog, you don't really have to get acclimated to "Sweet Jane" before it reveals its charms.  It hits you in the gut from moment one with its lean, mean riff, which lets you know it's destined for rock & roll immortality the moment you hear it.  (It's my personal favorite Reed riff, edging out "I'm Waiting for the Man" by a hair.)  
Nevertheless, Reed can't help himself from getting a little gritty, throwing in the suggestion that seemingly buttoned-up protagonists of the song, Jack and Jane, like to try on each other's clothes  (Jack's in his corset / Jane is in her vest).  To me, it was his way of pointing out that the mainstream is just as freaky as the fringe, even though outward appearances might lead you to believe otherwise.

"Sunday Morning" (The Velvet Underground)

"Sunday Morning" (1966) is probably the most commercial yet sneakily subversive track The Velvet Underground ever recorded.  It was written at the behest of producer Tom Wilson, who wanted a radio-friendly single to introduce the band and its German chanteuse, Nico, to the record-buying world before its debut album dropped.  Although the song was intended as a vehicle for Nico, Lou Reed ended up singing the lead vocal instead in a Nico-like whisper, turning in one of his more pitch-perfect performances.  (And a fine, folk-rock guitar solo to match.)
On its surface, "Sunday Morning" sounds as safe as milk: a dreamy, upbeat lullaby, replete with Sugar Plum Fairy-visions of John Cale tinkling around on a celesta that happened to be in the recording studio.  Under its pleasant exterior, however, is an examination of anxiety and regret felt after a night of indulgence.  Reed delivers the vocal with such reverence it's easy to miss that he's not singing about waking up to church bells chiming outside his window.
Subject matter aside, the track has a memorable melody (the kind that you find yourself humming inappropriately on a crowded subway train) with lush, reverb-y production work by Wilson.
Anyone who bought the single thinking it was representative of the full album was in for a very rude, R-rated awakening.

"I'm Waiting for the Man" (The Velvet Underground)

Ah, Lou Reed.  If there's anything that you could count on, it was that he was predictably unpredictable.  (I mean, did anyone expect his disastrous collabo with Metallica, Lulu?)
Read anything about him, and you'll find that music journalists loathed interviewing him.  He was touchy, mercurial.  The only interview I've read that actually went well with Reed was a 1992 piece by writer Neil Gaiman.  
So why did people bother going back to the well, time after time, if the water was tainted?
All you have to do is listen to his storytelling on "I'm Waiting for the Man" from the groundbreaking, Andy Warhol-produced Velvet Underground & Nico (1967), and it becomes clear: he was the poet laureate of society's fringe.  Half participant, half reporter, he captures a gritty tableau of someone traveling from lower Manhattan to Harlem to buy $26 of heroin from his dealer (the "man"), who is consistently late.
For as immediate and rocking as the song is (it really is the blueprint for every punk garage band that followed), it's decidedly bleak, even though it's gracious in its reality.
Put it this way, if the song "Heroin" from the same album is the idealization of the drug, "I'm Waiting for the Man" is the harsh truth: it's a parasite that leaves you waiting in stairwells of rundown brownstones for a pricey hit of fleeting euphoria, inevitably followed by lingering hell.  (And they released that as a pop single.)
Thing is, Reed never judges or wags a finger.  He wasn't about that.  He was more about: here's the facts; make of them what you will.
And if you've wondered, like I have listening to Velvet Underground & Nico over the years, are half of the stories and characters that pop up in Reed's literate rock & roll true?  Here's what he told Gaiman in 1992:
"It's always kind of funny, over the years, people continuously asking me, 'Are these things based on reality?'  I thought it was so obvious that they were."