For more roots of modern alternative, how about some late '60s / early '70s proto-punk?
New York Dolls - New York Dolls
The Stooges - Funhouse
MC5 - Kick Out The Jams
The Modern Lovers - The Modern Lovers
The Velvet Underground - The Velvet Underground and Nico
I tend to be pretty ideosyncratic in my music tastes and have followed few artists from album to album. That said, here’s my list, in no particular order.
U2, Auchtung, Baby. Blew me away from track to track. It’s got the hits like “One” and “Mysterious Ways”, a beautiful love song for drunks (“Trying to Throw Your Arms Around the World”) and some neat sounds courtesy of Brian Eno. Speaking of which…
Brian Eno and David Byrne, My Life in the Bush of Ghosts. Can’t explain this one, but it’s weirdness squared. Includes bonus exorcist of a Jezebel, set to music.
Johnny Cash I love the American albums, but I would suggest looking into Number 4, “The Man Comes Around” for its mix of Cash-penned numbers (title track with its Biblical apocalyptic theme) and “songs the kids like” (like “Hurt” and “Personal Jesus”). Try not to cry when he ends the CD with “We’ll Meet Again.”
Louis Armstrong Try a greatest hits package. I had acquired a three-disk set of swing music, listened to it once, and realized that after three tracks, it all sounds the same. Armstrong’s distinctive voice and trumpet cuts through that buzz like Mufuni through a samurai. An American original, in the best self-made way.
Jesus Christ Superstar It’s the beat, man, the beat. I love the original London stage recording with Murray Head and Yvonne Ellman. Big thrill for me was being part of the 39 Lashes scene in a local production, although my favorite is the vaudevillian Herod’s Song (“So if you are the Christ, you’re the great Jesus Christ / prove to me that you’re no fool / walk across my swimming pool”).
The Clash, London Calling
Stevie Wonder, Talking Book
Stevie Wonder, Songs in the Key of Life
Bruce Springsteen, Born to Run
Prince, 1999
Prince & The Revolution, Purple Rain
U2, The Joshua Tree
Talking Heads, Remain in Light
Michael Jackson, Thriller
Joni Mitchell, Blue
Joni Mitchell, Court and Spark
The Beatles, Revolver
The Beatles, The Beatles (The White Album)
The Beatles, Sgt. Pepper’s Lonely Hearts Club Band
The Beatles, Abbey Road
R.E.M., Murmur
R.E.M., Automatic for the People
Simon & Garfunkel, Bridge Over Troubled Water
Elvis Costello, Get Happy!!
The Police, Synchronicity
I’ve not heard Geogaddi yet but reports are it is similar. And yeah, I’d say more than one listen is required, as there’s a lot of stuff going on in the mix.
I know I’ve mentioned it on here twice or thrice before, and it’s not alternative, but Korong by Kornog is the absolute best album of Breton music in existence, and one of the very few albums I would call absolute perfection. I cannot recommend it highly enough.
Other essential albums in various genres:
Spiritualized, Ladies and Gentlemen We Are Floating in Space
Shudder to Think, Pony Express Record
Poe, Haunted
Type O Negative, Bloody Kisses
The Flaming Lips, any and every album from Transmissions from the Satellite Heart until the present day
Somebody earlier recommended Monster Magnet’s Powertrip, but I think that’s a little too stripped-down an album; Dopes to Infinity would be my choice there. Likewise, with Neurosis I think Times of Grace or Enemy of the Sun are better representative albums than A Sun that Never Sets.
Teletubbies: the Album is an outstanding example of the black metal genre.
American Pie by Don McLean I remember when I was young, the whole country sang the title song of that album for about a year. (albums 
)
Alice’s Resturant by Arlo Guthrie But thinking about it, if you never carried a draft card, you wouldn’t really appreciate it, that’ll change, keep an eye on Taiwan.
Well, I’m trying to spread the Wilco love, so I’m going to suggest Summerteeth and A Ghost is Born.
Luckilly, I’m up in the Great White North.
Wow, thanks for all the responses so far. While there have been a couple of albums that I’ve already own, 90% of the stuff is new to me.
Special thanks to ultrafilter for that amazing metal breakdown and pepperlandgirl for the Wilco.
I love this board. 
Jeff Buckley - Grace
Man, I was just coming in here to recommend Amon Tobin. His alter-ego, Cujo, has a good album called “Adventures in Foam.” Really good stuff.
I like a lot of different types of music. Many of the above suggestions are very good (although I certainly couldn’t differentiate between so many types of metal). People who make lists like these tend to like music which is quite obscure, and to pooh-pooh Best Of albums. If you’re buying music, however, Best Of albums do have their place – who wants to buy a CD for one or two good songs?
Anyway, in no particular order, pulled off my musicmatch list… I like (alternative music included to see if tastes match, or to broaden exposure):
Before I get pissed on, I’m well aware that Best Of albums like “Beatles 1” aren’t as “good” as The White Album, Sargeant Pepper, Rubber Soul, Revolver, etc. Nor as good as 1962-1966 and 1967-1970. My list is to give you exposure to different bands, not buy their discography. Of course The Beatles are a bad example.
For early hip hop, consider Def Jam Records: 10th year anniversary (4 CDs).
You might want a best of Kenny Rogers, Classic Country, 50s songs, Bing Crosby, Tony Bennett, Frank Sinatra, Eric Clapton (esp, Crossroads), Charlie Parker, The Kinks, Disco, Pink Floyd (echoes), The Police, Mambo Music, Movie Music:The Definitive Peformance, etc. There is lots of good world folk music, country music, classical music and jazz my list was too brief to include.
Yer still a little light in the Rock/Jazz Fusion genre.
Might I suggest a little Cosmosquad and a little Jeff Beck.
Alice Cooper - Billion Dollar Babies and Killer.
You didn’t think I was going to suggest some other band, did you? :rolleyes:
I’m tired, so I’ll make this sort of brief in each respective category.
If you want to go into alt-rock history, I guess I’ll point out my favorite albums in that genre…
The Velvet Underground are essential. Pick up The Velvet Underground and Nico, it has Heroin on it. Their other albums are good too, but there is disagreement about them. I personally don’t like the second one White Light/White Heat. Their third album has a much gentler, acoustic sound. It’s called The Velvet Underground. I like that album a lot. My favorite song on it is Pale Blue Eyes, which I don’t think I had heard before I got the cd but it sounded so familiar.
Their fourth album, Loaded, is their poppiest. Some fans dismiss it as a sell-out album- it was made in response to people who said that VU couldn’t write a hit song. I like that one quite a bit too, and it has one of their best songs, Sweet Jane.
Lou Reed’s second solo album, Transformer, is also excellent. It was produced by David Bowie and Mick Ronson.
Speaking of David Bowie, you can’t forget him. He’s got a ton of essential albums. You should probably start with The Rise and Fall of Ziggy Stardust and the Spiders from Mars. It’s not my favorite of his, but it’s a great one to start with. Every song on it is great.
For now I’m gonna skip to '77 and the great albums there. There are a ton of great punk albums I could list, and I haven’t even heard all of the major punk albums that year.
For now, I’ll just mention Television’s album Marquee Moon. This is one of my favorite albums. They have a ton of melodic lead guitar parts interweaving throughout their songs.
I consider New Order to also be essential. I don’t have any of their early albums, just Substance, which is an excellent compilation of their early material.
Echo and the Bunnymen are another of my favorite bands. Any of their first four albums are great, but I most highly recommend Ocean Rain. It uses orchestration to a great effect.
REM’s albums Murmur, Reckoning, and Life’s Rich Pageant.
The Smiths- It’s hard to decide which one. Their most essential is probably The Queen is Dead.
I should get to bed now. I’ll fill in some of the gaps I left tomorrow.
Let me take you to the underground and I mean really deep underground…here is just one hip hop artist you should be checking out. BUSDRIVER
A strong recommendation here for The Blow-Up, the two-disc set of live Television recordings from 1978 that was released a few years back. It has some blistering work including a 15-minute “Little Johnny Jewel” as well as “Marquee Moon” and an excellent “Ain’t That Nothin’” that’s my favorite track.
On the subject of live recordings, I’d say Bob Dylan’s “Royal Albert Hall” concert is pretty damn essential. Go for the two-disc Bootleg Series version, which contains the first (acoustic) half of the show as well as the (electrified) second half that caused so much fuss. I’ve had a CD of the electric part of the show for years, but when I picked up the Bootleg Series version a couple of years ago, I found that listening to the discs in order really added a new dimension to the venom so openly expressed by some parts of the audience during the electric part of the show. Besides which, it’s just a kick-ass performance - that stretch of “I Don’t Believe You,” “Baby, Let Me Follow You Down” and “Just Like Tom Thumb’s Blues” is about as rockin’ as anyone could want, IMHO.
If you like strange music and want Hip-Hop, how about:
William Burroughs’s Spare Ass Annie
Strangest album ever.
Elvis Costello, This Years Model, punk
Richard Thompson, Daring Adventures, rock with a folk tinge
Dwight Yoakum, Guitars, Cadillacs, Etc., Etc., country