"Shake Your Rump" (Beastie Boys)

"Shake Your Rump" from the classic album Paul's Boutique (1989) is the line between "the old Beasties" and "the new Beasties" for me.  All you have to do is listen to the first :30 of the track, and you instantly know that the frat boy shenanigans of 1987's Licensed to Ill are a thing of the past.  In fact, they'd had a highly publicized split with Russell Simmons, Rick Rubin, and Def Jam Records in 1988, the result of the band wanting a bigger cut of the profits and more creative control.  This ultimately led to the Beasties relocating from New York to L.A. and hooking up with the production team of John King and Mike Simpson (a.k.a. The Dust Brothers).  It also spawned weird rumors that the band was defunct because Michael "Mike D." Diamond had died from an overdose.  (I can't help but wonder if Rubin and Simmons might have had a hand in spreading those very rumors.)
Anyway, Mike D. wasn't dead, as he addresses in the second verse of the song (Well I'm Mike D., and I'm back from the dead / Chillin' at the beach down at Club Med...).  And the Beasties weren't kaput.  In fact, their tag-team flows were even more intricate and filled with pop culture references than ever before: they namecheck everyone from Fred Flintstone to The Brady Bunch's Sam the Butcher on "Shake Your Rump."  
On top of that, the song introduced the world to a whole new way of sampling recorded material.  No longer were the Beasties just copping some Black Sabbath riff and looping it over a single Led Zeppelin breakbeat; the track was one, big sound collage (there are at least one dozen identified samples on the track), culled from a vast library of vinyl and pieced together in completely unexpected ways.  It was as inventive as it was funky.
My favorite moment of this song is still that first instance when DJ Hurricane scratches in Afrika Bambaataa saying Shake your rump-ah! from his 1984 collaboration with James Brown, "Unity, Pt. 2," and then segues into that fantastic Moog synth growl from Rose Royce's "6 O'Clock DJ (Let's Rock)" from the Car Wash soundtrack.  It's still as fun and fresh as it was in 1989.

"Sabotage" (Beastie Boys)

"Sabotage" from Ill Communication (1994) embodies why the Beastie Boys were/are pop culture icons.  Not only did they take elements of hardcore and rap and meld them into something completely vital and fresh, but they also dreamed up the premise for the track's iconic video, which gives props to 70s cop show cheesiness in all its low-budget glory.
I can't listen to this track without immediately thinking to myself: "Starring Nathan Wind as Cochese."
A bit of history: "Sabotage" began its life as an instrumental jam.  As producer Mario Caldato, Jr., reminisced to Sound on Sound in August 2013, Adam "MCA" Yauch (R.I.P.) was fooling around with his Superfuzz effects pedal when he came up with the song's bass riff.  Long story short, the rest of the band (including percussionist Eric Bobo and keyboardist Mark "Money Mark" Nishita) heard what MCA was putting down and joined him in jamming.  After they'd gotten the hang of the groove and did some quick arranging, they committed the song to tape.
But as Caldato points out, the Beasties were wary of the track at first.
"When we first played it back, the guys were saying, 'It sounds too rock. We don't really want to go down that route'."
After all, they'd spent 7 years trying to distance themselves from the frat boy rap-rock of 1987's Licensed to Ill.
So the track sat around for awhile and almost got shelved, until Adam "Ad Rock" Horovitz called up Caldato one day, saying that he had an idea for lyrics.
Caldato recalled that Horovitz came over to his house in L.A. and cut his vocals in a single afternoon using a handheld mic.
"It was perfect.  He had done his homework, and he was screaming it with the exact amount of energy and attitude needed."

"Sure Shot" (Beastie Boys)

If someone were to ask me, "What makes for a great hip-hop sample?" I'd probably say a funky breakbeat, distinctive bassline, or maybe an infectious horn riff.  But "jazz flute solo" would not be at the top of my list.  

But I can't imagine the song "Sure Shot" without that flute wailing away as the Beasties holler You can't, you won't, and you don't STOP...

If you owned a copy of 1994's Ill Communication (more on that in a sec), you know from the liner notes that the sample comes from a semi-obscure tune called "Howlin' for Judy" by New York-based jazzman Jeremy Steig, who is the son of the late, great illustrator William Steig—the originator of Shrek.  A quick listen to "Howlin' for Judy" reveals that the Beasties really only sampled 3 seconds of the song for "Sure Shot"; the rest of the track is sort of a day-glo freakout with overdubbed flutes coming at you from about five different directions.  It's oddly funky...in a Ron Burgundy kind of way.

In a 2004 interview with All About Jazz online, Steig was asked how he felt about the group sampling his 1969 track.  His response: "I made more money from that sample than from any of my records."

Anyway, Ill Communication was the first CD I ever bought.  (It wasn't the first album I ever bought, though.  That was actually Kick by INXS.)  

I'd gotten a Discman with car audio adapter from my dad for my 17th birthday.  It was an awesome gift.  Although, I think he was even more excited about it than I was!  I'd barely even finished tearing off the wrapping paper, and he had the box open and was busy plugging the various cords and adapters into my car's tape deck before I even had a chance to touch it!

I remember him sitting there in the passenger seat of my car like an impatient kid. "Well, come on!  Test it out!"

One minor problem: I didn't own any CDs.

My birthday falls about a week before Christmas, so I had no desire to go fight the crowds at the mall, just to go buy a CD.  Besides, I had a stack of mix tapes in my car with hundreds of hours of music on them, so I was content to wait till the New Year.

A couple of days later at the start of Winter Break, I was having a leisurely breakfast, when Dad informed me that I'd be driving him to Asheville Mall later that morning to help him finish his Christmas shopping.  Which I did.  Through an hour of bumper-to-bumper traffic, fighting kamikaze soccer moms in minivans who would rather go down in flames than let you merge in front of them, because God forbid you should get to that sale at Penney's before them.

Long story short, Dad made one lap around Sears, decided they didn't have the socket wrench he supposedly was going to get my uncle, and headed right for the music department at Montgomery Ward.  And in perfect Dad fashion, he said, "So, what did you need to buy here?"  As if the mall had been my plan all along.  

I dropped $9.99 of my birthday money on Ill Communication.  (Confession: I wasn't even that big of a Beasties fan at the time.  It was just one of the few CDs that was on sale, and it had a couple of songs I liked.  But my opinion of the band's talent and importance in the hip-hop world completely changed after one listen.)  It's a CD my father wouldn't have chosen in a million years.  Even so, he couldn't wait to hear it on my new Discman.  And "Sure Shot" was the first thing we heard pouring from my car speakers, sitting there in the mall parking deck.

"Not bad," I remember him saying.

"Shadrach" (Beastie Boys)

Back in 1989 when the Beastie Boys' Paul's Boutique was released, no one really knew what to make of it.  See, there were two rumors circulating at the time: 1) Michael "Mike D." Diamond had died from some kind of overdose, and 2) the followup to the group's multi-platinum License to Ill (1986) was nothing more than snippets of unfinished tracks that had been remixed and rush-released to capitalize on Diamond's untimely demise.
But Mike D. wasn't dead.  And Paul's Boutique wasn't just some odds-n-ends pastiche of recycled rhymes about frat boy buffoonery culled from demo tapes, thoughtlessly slapped on top of random beats—despite what some music critics and gossip-mongers claimed.
It was a groundbreaking exploration of sound that took sampling to new heights.
One of the key tracks on the album is "Shadrach," a stanky chunk of funk, primarily built upon a sample from Sly & The Family Stone's 1974 single "Loose Booty," that features tag-team rhyming and mile-a-minute pop culture/autobiographical references.    
The title, "Shadrach," not only refers to the chant that Sly and Freddie Stone repeat, ad infinitum, in "Loose Booty" (Shadrach, Meshach, Abednego...), it's also an allusion to the three Biblical brothers (Shadrach, Meshach, and Abednego) who were saved by an angel of God after being thrown in Babylonian King Nebuchadnezzar II's furnace for refusing to bow to an idol.
It's actually the latter that has the most to do with the Beasties' lyrics.
They were three guys who'd been vilified by the mainstream media across the globe for their (satirically) offensive rhymes and (comedically) loutish behavior.  At the same time, they had sold tons of records based on their "scream loud/drink beer/break shit" image—an image that Def Jam Records chief Russell Simmons wanted them to perpetuate to keep the cash wagon rolling.  Thing was, the Beasties were tired of playing drunken caricatures of themselves, so they broke their contract with Def Jam and Simmons's Rush Management, which led to years of legal wrangling.  Nevertheless, they gained artistic autonomy and started over in LA with producer Mario Caldato, Jr., and crate-diggers extraordinaire The Dust Brothers (John King and Mike Simpson) helping them chart a new course.
So they had been through the fire, and they had not only survived, but they'd also remained true to themselves.

"Intergalactic" (The Beastie Boys)

By the time "Intergalactic" dropped in 1998, The Beastie Boys had already covered quite a bit of ground musically.  They had gone from being a punk band to becoming a tongue-in-cheek frat boy hip hop outfit, and then explored new dimensions in sampling with the Dust Brothers.  They also dabbled in D.I.Y. funk and acid jazz.  Then when the boys' quirky amalgam of hard rock and hip hop, which comprised a good chunk of the music on Check Your Head and Ill Communication, woefully spawned shitty imitators like Limp Bizkit and 311, they changed things up and reinvented themselves again on Hello Nasty as alt rock/hip hop futurists.  (And the future apparently had b-boys breakdancing on the moon in vintage Adidas track suits and smoky Martini bars, where the servers all were Rosie from The Jetsons...)
But little prepared the world for the vocoded robot voice dropping science in "Intergalactic's" intro.  Or the quirky sample of Les Baxter's Moog rendition of Rachmaninov's Prelude in C# Minor burbling under the track.  Or the ol' skool tag team vocal approach that felt fresh off a Sugar Hill Records joint (or just altogether fresh).
Nobody else could have pulled off a song that mixed nostalgia for 1960s budget sci-fi flicks and the Boogie Down Bronx circa 1979 with Year 2000 fervor like The Beastie Boys.
Nobody.