"'Heroes'" (David Bowie)

David Bowie had gotten his fill of fame and its vices.  So he left the glitz and drugs behind and relocated to Berlin in 1976, drawn by the city's Cold War-era austerity.  In time, he was joined by longtime collaborator/producer Tony Visconti and musician Brian Eno and, together, they created a trilogy of challenging, groundbreaking albums (Low, 'Heroes', and Lodger) that still sound unbelievably fresh today.
All three records, incidentally, were recorded at Hansa Studios, which sat within view of the Berlin Wall, or the "Wall of Shame" as it had been dubbed by the West.  One afternoon while staring out the window of the studio's control room, Bowie happened to catch Visconti passionately kissing a young woman (who wasn't Visconti's wife) beneath a guard turret on the Wall.  On the one hand, Bowie saw their act as heroic: they weren't allowing the very real danger of being shot by guards deter them from freely expressing their very real affection for one another.  On the other hand, he surmised that they were meeting in such a dangerous place because they felt guilty about the affair, and they were psychologically justifying their rendezvous as an act of "heroism."
The incident inspired Bowie to pen "'Heroes'", an intensely emotional, complicated portrait of ill-fated love winning a victory over oppression for a fleeting moment (hence the ironic quotation marks in the song's title).  
Although every note of this song is electrifying, my favorite moment comes in the second verse, as Bowie nearly cries the words And the shame was on the other side.  It's such a smart bit of wordplay, referring not only to the lovers' literal location in the shadow of the "Wall of Shame" but also the feelings of self-reproach that they're attempting to put aside.
In short, this is the song that made me a Bowie fan for life.

"Needles in the Camel's Eye" (Brian Eno)

"Needles in the Camel's Eye" is a song about nothing.  Really.  Brian Eno strung a bunch of words together because he liked the way their vowels sounded.
For anyone looking for deeper meaning, Eno had this to say: "I regard [the song] as an instrumental with singing on it."  (FYI: That quote's pulled from Eric Tamm's 1995 book Brian Eno: His Music and the Vertical Color of Sound.  It's one of the most academic, utterly boring books about a rock musician I've ever encountered.  So, if you're having trouble sleeping...)

Sonically, it's an electronic tidal wave of noise that rocks like a Carl Perkins song as reimagined by a Martian garage band.  The guitars crank away, creating a metallic mist.  Synths sizzle and hum in the background.  And the drumming is like a junior high marching band trying desperately to count to "four."
In other words, gloriously sloppy and invigorating as hell.

"Crosseyed and Painless" (Talking Heads)

There was no band in quite the same league as Talking Heads from 1977 to about 1984.  If you've never seen it, watch the concert film Stop Making Sense (1984).  Fair warning: if you don't already own every album in the band's discography before watching the film, you will purchase every album subsequently.  (It's worth your bank account taking a hit and you having to eat Ramen for a few weeks.  Trust me.)
My favorite Talking Heads album, Remain In Light (1980), falls smack-dab in the middle of that golden period of output.  The album is a non-stop tour de force of memorable melodies, polyrhythmic percussion, highly abstract yet highly literate lyrics, and producer Brian Eno's experimental sampling and tape loops.  It sounded like nothing else in 1981, and it still sounds otherworldly today.
Although it's difficult to pick out individual faves from the album, "Crosseyed and Painless" is a track that definitely shines.  The song is built around an Afrobeat rhythm, with cowbells and various percussion loops creating this undulating groove behind Chris Frantz's relentless drums and Tina Weymouth's gulps and slaps of fat bass.  (Side note: that woman must have callouses on her thumbs the size of grapes.)  It also features a guest spot by King Crimson guitarist Adrian Belew, who releases a buzzbomb guitar attack in the middle of the song.  (It's not a showboating type of guitar solo; nevertheless, it soars and wails in all the right places.)
Then there's frontman David Byrne's characteristically nervous vocals and a somewhat surprising "rap" at the end of the song (Facts are simple and facts are straight / Facts are lazy and facts are late...), which was inspired by Kurtis Blow's "The Breaks" (1980).
The song was released at the time as a promotional single with an accompanying video by choreographer Toni Basil (of one-hit-wonder "Mickey" fame), who used a Fresno, CA-based breakdance troupe known as Electric Boogaloos for the shoot.  I remember seeing the video ONCE on MTV2 sometime in the late 90s at like 2 am, and I didn't want it to end; it was like being zapped back to my childhood. 
I finally found the original video again on the interwebs for your (and my) enjoyment.
(P.S.  Dig the guy doing the moonwalk--a.k.a. the "backslide"--at the 3:30 mark, almost three years before Michael Jackson "debuted" it on the Motown 25 TV special!)

"Here Come the Warm Jets" (Brian Eno)

I have an enormous amount of respect for Brian Eno as an artist.  If you need an example of "thinking outside the box," look to Eno.  
On second thought, don't.  
With Eno, there is no box.  Never was.  There was a rhombus covered in fluorescent lights once, but he set fire to it in the 70s.  
He's refused to be bound by any one genre or particular sound.  Yet, anytime you hear anything that he's written, recorded, or produced in the past 40 years, you can only describe it as "Eno-esque."  It's that singular, off-kilter approach to pop songcraft.  It's a synth coming in where you'd expect a drum.  A guitar that shrieks like a cat in a blender.  A piano that sounds like a nightmare come to life.  An angelic, electronic choir that blasts affirmation of life.  And sometimes all of that is within the same 4-minute song.
On the title track from his 1974 album, instruments lose their identities and intertwine in a fuzzed out fanfare that sounds like a victory song played by an army of Huns.  Or maybe a drunken lot of football fans.  
At first I wondered, is that synthesizer?  Is that guitar?  Then I realized that question was irrelevant.  It's an atmosphere.  It's a feeling.  It's a warm jet!
What's a warm jet?  
Pffft.  Irrelevant!
Whatever it is, it stirs stuff deep in your gut that makes you want to punch the air.  
Then these drums that sound like a stampede march in from all sides, carrying a faint hint of a vocal that turns into a muddy chorus of Enos, singing about...  Um.
Something about being on your knees?  Something about saints?
Whatever he's singing, it sounds like revolution and triumph.
Sounds, sounds, sounds.
That's Eno.