There’s a reason The Dark Side of the Moon stayed on the Billboard album charts for more than 14 years. If the OP is going to listen to any Pink Floyd album it has to be this one.
Update
**Guns N’ Roses - Appetite for Destruction
**
Holy crap. This is the definition for what I was hoping to find by doing this. This was unbelievably good. Consider my mind blown. Completely blown.
This is a debut album? These boys sound like they’ve been in band for years and years. I can’t believe they produced this the first time out.
Home run. Grand slam. The best album I’ve heard on this little journey.
This one is getting a permanent spot on my Ipod.
Loved it! I’m smiling just thinking of how good this album was. Wow.
I have to add my voice to the Dark Side of the Moon chorus. If you’re only going to listen to one Pink Floyd album, it should probably be that one. Every song on it is a good song, and each one moves the record forward. It’s probably one of the first records I’d heard that when side one was over, all I wanted to hear was side two.
Conversely, I’d only recommend The Wall if you’ve got everything released before it, and even then there are a lot of Psychedelic/Progressive albums I’d rather listen too beforehand.
Beware: It’s a damn good record, I wore out the copy I got when it was new. However, they’re one of those bands that probably should have broken up after their first record. Purchase the rest of their catalog with extreme caution.
I would argue that every song on the first three sides of The Wall are good songs. It trails off a bit after that, but nearly every song, even the throwoff songs, have great soloes. If you want to hear blues-rock twinged* ripping guitar soloes along with good lyrics, The Wall’s your choice (if you just want to hear good blues-rock-ish music, Obscured by Clouds is also good but that doesn’t fit the thread in that “everyone” hasn’t heard it.)
*with just enough je ne sais quoi to put it in a class all of its own.
I’ll preface this by saying that Warren Zevon is one of my all-time favorite artists and the inspiration for my screen name. 
The best place to start would be Excitable Boy. It contains:
Werewolves of London
Roland the Headless Thompson Gunner
Lawyers, Guns and Money
Excitable Boy
Johnny Strikes Up the Band
Accidentally Like a Martyr
The compilation A Quiet Normal Life contains these songs (“Lawyers, Guns and Money” is, unfortunately, the censored version) in addition to:
Desperados Under the Eaves (my favorite)
Mohammed’s Radio
Play it All Night Long
Poor, Poor Pitiful Me
I’ll Sleep When I’m Dead
That’s where I started with Zevon. Genius is also very good: it has most of the above along with Mr. Bad Example, Carmelita, Hasten Down the Wind, Mutineer, and his cover of Raspberry Beret with R.E.M.
The Warren Zevon/R.E.M. collaboration was called Hindu Love Gods. Buck, Mills and Berry were also Warren’s backing band for his Sentimental Hygiene album. The only thing I didn’t like about Genius was that it didn’t include “Desperados Under the Eaves.”
2nd choices for Zevon: either Bad Luck Streak in Dancing School, highlights being Jungle Work, Gorilla You’re a Desperado, and Jeannie Needs A Shooter, great guest guitar work by Joe Walsh (if you like that kind of thing.)
Or, Stand In The Fire, a live recording of many of his best songs.
Speaking of Joe Walsh, the James Gang live in concert album is really good.
Regarding Zevon, A Quiet Normal Life is not a bad place to start, but it’s woefully short. If that whets your appetite at all, my suggestion would be to seek out I’ll Sleep When I’m Dead, which is out of print but available used; it’s simply the best anthology of Zevon’s oeuvre. After that you can do what I did, and pick up the remastered/expanded edition of 1976’s Warren Zevon and then the albums not covered by the anthology: Life’ll Kill Ya (2000), My Ride’s Here (2002), and The Wind (2003). (Why, yes, I did get just a little . . . obsessed with his music for a while.)
Did Queen have “phases” or “periods”? I’ve listened to Night at the Opera 1 1/2 times now and surprisingly, I’m not a huge fan. Oh, I like some of the songs, but it doesn’t sound like the band I expected.
This is the first band in this little experiment that I’ve kind of been familiar with. I have listened to “A Kind of Magic” a few times since it goes with the Highlander, one of my favorite 80’s movies. I love most of the songs on Kind of Magic, but it sounds like a different band to me…or at least the same guys who are way different.
I’ll post full thoughts on Opera later, but I’m considering trying a Queen album from the mid or late 80’s.
Just skipped through the thread so here are a few suggestions:
Blodwyn Pig – Ahead Rings Out: seminal early British rock
Cream – Best of Cream has most of their good stuff.
You could also try Blind Faith which was the successor to Cream. Aficionados swoon (and I have the vinyl only a few feet away) 
Jethro Tull – Aqualung. This is one of the core albums of all time.
Yes – Close To The Edge
Lou Reed – RocknRoll Animal. Much as I appreciate the Velvet Underground, this is still the definitive album.
Emerson Lake and Palmer – Trilogy. The alternative rock high point with gentle songs and soaring moog organ.
Uriah Heep – Very Eavy Very Umble (borrowed from Charles Dickens).
Just as important as above, The Who – Live At Leeds. This again is high point in rock and has to be played loud. Preferably with incense and lightly altered state of mind. Every live album since tries to emulate this.
And for balance here are a few different albums:
Renaissance - Ashes Are Burning. This is enduring folk rock and still bought today.
Elton John - Madman Across The Water. Elton is probably best known for his later work and shows which are fine but this is a beautiful gentle album. His best.
Elton John - Yellow Brick Road. Sometimes forgotten because its decades old but again, a beautiful collection of music. His next best and that’s saying something.
Crosby Stills Nash and Young - Deja Vu. Essential. Enough said.
Woodstock. I am watching the movie as I write. If you wish to immerse yourself in the early rock era this is the place to go. Bored, just skip to the next artist. See Me Feel Me…
The Sex Pistols - Never Mind The Bollocks. Punk was a reaction against the established music industry - the Stones, the Who, Deep Purple etc. Raw and energetic.
Ah sod it, I’m watching Rodger Daltry do his thing so a few more…
Deep Purple - Deep Purple In Rock. This is another of those 10 albums of all time which signify and illustrate the core of rock.
Deep Purple - Machine Head. Just do it.
The Who - Who’s Next. An album perhaps 20 years ahead of its time. The first track Baba O’Riley is used on the show CSI today. Mistakenly called “Teenage Wasteland”.
While I’m waiting for Jimi to take the stage, I’ve avoided two giants of rock.
Black Sabbath and Led Zeppelin.
The first four albums from both bands are essential listening.
The Queen of A Kind of Magic is definitely not the same as the Queen of A Night at the Opera (qualitatively, that is; same personnel, different sound) – nor is the Queen of the 80’s the same as the Queen of the 70’s, the watershed probably being the aforementioned The Game (1980). I’d recommend it though (The Game, that is), especially if the latter years of the band are what you’re more familiar with. It’s a bit more commercial and pop-influenced than their earlier albums, but still rocks. “Another One Bites the Dust” is the track everyone knows, or “Crazy Little Thing Called Love”, but you can also find such rockers as “Dragon Attack”, “Rock It (Prime Jive)”, and “Need Your Love Tonight” there.
And if you liked Appetite for Destruction that much, I would seriously suggest you look at Guns N’ Roses’ precursors already mentioned: namely AC/DC, Aerosmith, vintage Rolling Stones, Who, Led Zeppelin. Nothing wrong with Guns (and I like that album an awful lot, too), but these guys established the form.
I’ll take some suggestions right now, though my queue is getting rather long. Here is what I know.
Aerosmith - Zippo except “Dude looks like a lady” from Mrs. Doubtfire. I had to be told what band that is. I know who Steven Tyler is, though…he kind of permeates the culture. What album is their classic?
AC/DC - I know nothing of this band. Well, I think they have a song called Hell’s Bells or something, but I’m not even sure of that.
Rolling Stones - I’ve heard “get no satisfaction” and I know who Mick Jagger and Keith Richards are(they also permeate into the culture). I think I have heard other songs because they are so famous, but never an album.
Led Zeppelin - They made Stairway to Heaven. That is all I know.
I just love the creamy guitar sounds on Queen’s records. You can absolutely recognize it anywhere.
So many great suggestions… I have to add Joni Mitchell either Blue or Court and Spark, (Court and Spark being my favorite) and Marvin Gaye’s ***Live at the London Palladium ***
I’ll agree with Just Ed that these are all bands you must check out if you liked Appetite for Destruction so much; but I’ll leave the specific recommendations to others more familiar with their complete works.
Eeesh. Well, “Dude” is from Permanent Vacation (1987), which is not a bad album (notwithstanding “Dude” being close to a novelty track; it was their “comeback”), but is probably not the best place for an overview of their sound. Their classic would be either Rocks (1976) or Toys in the Attic, (1975), but Greatest Hits 1973-1988 is a great overview (it’s an expansion of an earlier collection from 1980).
“Hells Bells” is from the already-recommended Back in Black (1980), which is a damn good place to start with AC/DC – though I wouldn’t argue with Wordman that Highway to Hell (1979) is criminally overlooked at times. Those two albums probably represent the pinnacle of AC/DC’s output, which is singularly exceptional in that they changed lead singers in between (Bon Scott died after Highway and Brian Johnson stepped in for Black).
The Stones are one of those bands that have not only an impressive catalogue of studio albums behind them, but an imposing array of compilations as well. I’m not sure what would be the singular classic Stones album (Sticky Fingers or Exile on Main Street are the most likely contenders), but I would definitely recommend an overview here - Hot Rocks (1964-1971) is a great collection of their early years, and you could go on to individual albums from there if you liked (particularly since the collection pre-dates Exile).
Led Zeppelin. Well, like Accidental Martyr and Zevon, here I’m somewhat biased in that Zep is by far my favorite band, period. They actually do have a couple of “greatest hits” collections (Early Days and Latter Days), but they were very much an “album-oriented rock” band, and their albums were all very strong. “Stairway to Heaven” is on their fourth, released in 1971 (technically untitled but typically referred to as IV or Zoso), not a bad place to start, though II (1969) is somewhat closer to the hard rock sound of Appetite for Destruction.