Let’s pretend I didn’t have my mind somewhere completely else and screw up the coding.
Opera.
*Rigoletto *or Carmen.
Elliott Smith - I guess I would choose XO, as it is simultaneously his best and most accessible album, even though my favorite songs are spread out amongst his other albums.
Nellie McKay - All of her three albums are a mix of great, good, and so-so, but I would start with her first (Get Away From Me), which showcases her extremes pretty well, including her delving into rap.
Radiohead - OK Computer FTW. No question, one of the greatest albums ever, was great to hear the first time, and great to hear the 500th time.
If I wanted to introduce someone to The Brilliant Green, with only one disk, I’d be VERY torn as to what to do it with.
Obvious choices, as broad overviews of the band, would be the Complete Single Collection (which I don’t have, and don’t intend to get, since Ash Like Snow is the only single I don’t have, yet), or the Super Terra 2000 DVD. Unfortunately, the Single Collection only has the title track from each single, and for most of them, I think the ‘b’ track is better. And Super Terra 2000 is a live performance, so many of the tracks sound noticeably different than the studio versions - for instance, Tomoko does a screamy thing on Bye! My Boy! and Baby London Star, which, while having some charm in the live setting, she doesn’t usually do, and doesn’t show off her voice well.
Discarding those, I think, the best bet would be Terra 2001. Not only does it have more of my favourite songs than any of the other albums, it’s the strongest AS an album.
The Soft Boys Underwater Moonlight I prefer A Can of Bees but Moonlight is easier on the ear.
Steely Dan NOT Aja, lets go with The Royal Scam.
The Beatles (this is hypothetical I hope) Hard Day’s Night not Sgt Pepper.
Arrrrrgh, I am seriously torn. IV is great, but I (for Your Time is Gonna Come / Black Mountainside) or II (Ramble On and the Lemon Song) would also be great introductions. I have a seven-month-old boy now, and someday I’m going to have to choose which Zeppelin album to put on for him first… and I think it’s going to be I or II. Stairway is a symbol because people know it, but if you’re truly introducing a stranger to a song, I don’t think it holds up as well as Ramble On.
Of course that means he would have to wait until I put on IV to hear When the Levee Breaks… which would be a crime.
Jurph, if he’s seven months old, shouldn’t you have had him listening to Zep for like, almost 16 months already? My dad had me listening to Yes, Pink Floyd and Jethro Tull when I was still in the womb.
Thanks for the rec, Equipoise. I’ll definitely give her a listen. 
Guster
Lost and Gone Forever is my favorite CD from the band, but I think Keep It Together is the most accessible to new listeners. Although I did use Ganging Up on the Sun to get someone into them just the other day because it was what I had around.
Geinoh Yamashirogumi - Akira
Their other music is all very good as well (except some pop-chorus stuff), but Akira really is the one with the most range and overall skill put into it.
Well for a kid, I would go with the Rain Song.
In fact for the Beatles, I accidental made both kids Beatles fans by playing the Yellow Submarine movie as often as they wanted, which was very. 
They both recognize Beatles and one even mistook a Monkey song for Beatles.
Neither of them like Led Zeppelin yet, but my son already loves Queen.
Peter, Paul & Mary are popular and my daughter likes the Indigo Girls, Tracy Chapman and similar female folk rockers.
I know for Zep, I started with Zep I as my older sister had bought it when I was only six.
DJ Shadow - The Private Press for sure, it’s the most consistently approachable of his three albums (and my favourite if I’m listening all the way through, rather than to select track). The real gems live on …Endtroducing, though.
Death Cab for Cutie - Transatlanticism is my favourite, by far, but I generally start people off with Plans, since it has a bit more major label polish.
Elliott Smith would definitely be XO, as Windwalker already mentions below, though I tend to introduce newbies to Elliott by giving them a track or two at a time instead of a whole album.
**BT ** (Brian Transeau)
Primarily electronic dance music, but works with or has worked with other artists, such as Tori Amos, Britney Spears and Tiesto.
This CD is a bit more mainstream, but it is my favorite so I’d have to go with “Emotional Technology”. Every song on the CD is great, but my favs from it are: Force of Gravity, Superfabulous (w/Rose McGowan), and Somnambulist.
If you’re looking for some other samples of his music, another of his CDs *Movement in Still Life * is really good as well.
Hm. REM’s probably my favorite band–or up there–and Document is my favorite album of theirs. But if I’m going to introduce someone to the music, I’m more likely to show them Automatic for the People.
Likewise, I love Gogol Bordello. My favorite song by them is “Not a Crime.” If, however, I’m introducing someone to them, I show them “Start Wearing Purple” first.
Dead Can Dance - have to go with Aion - the most balanced combo of instrumental, Brendan and Lisa songs, with my absolute favourites Saltarello, Fortune Presents… and Song of the Sybil. Misses some greats like *Cantara *or Ulysses, but can’t have everything, now can we?
Joy Division - damn, hard to choose, but I think Unknown Pleasures has it over Closer, even if it’s not my favourite of the two. It is the less personal of the two, and for introducing someone to the band, I think it’s the more accessible (it was for me)
The Smiths - my fave’s The Smiths but I think The Queen is Dead is the best intro to the band - mature, not as angry as Strangeways…
This all assumes compilations are out otherwise we’re looking at *A Passage In Time *, Substance and Louder Than Bombs, respectively.
I don’t have a favorite band, but I can toss off (not what you think, you kinky brits)a few classics for the heck of it. In no particular order:
Cheap Trick - Cheap Trick
The Jam - All Mod Cons, Setting Sons, or Sound Affects
Loud Family - Interbabe Concern
Starz - Starz
Bram Tchaikovsky - Strange Man, Changed Man
Buzzcocks - Singles Going Steady
Undertones - Undertones or Hypnotised
Plimsouls - Plimsouls (hard to find)
Silos - Cuba
The La’s - The La’s
The Kinks - …are the Village Green Preservation Society
The Psychedelic Furs - Talk Talk Talk
Thin Lizzy - Jailbreak
Midnight Oil - 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
AC/DC - Let There Be Rock
Rose Tattoo - Rose Tattoo
I’m sure I forgot more than I remembered… :o
The Tragically Hip - Most people prefer Day for Night (which isn’t even in my top 4), but I’d start someone with my favorite, Fully Completely, as it’s a good idea of their rock sound. After that, I’d suggest the blusey/rock of the album prior, Road Apples.
Their signature song is “New Orleans is Sinking” which is on their first full-length album, Up to Here, which is raw, unpolished rock.
I would *highly * recommend catching a show since a lot of their songs sound even better live. They are easily the best live band I’ve seen and lead singer Gordon Downie is fantastic to watch. He’s absolutely batshit insane on stage.
My Top 10 “must have” albums: (limiting this to 1 per artist)
The Clash - London Calling
The Smiths - The Queen Is Dead
Radiohead - OK Computer
New Order - Substance
Violent Femmes - Violent Femmes
Stone Roses - Second Coming
Clinic - Internal Wrangler
REM - Eponymous
Depeche Mode - Violator
U2 - Achtung Baby
Sunstance and Eponymous are kind of like “greatest hits” albums, but they’re really good.
The Alan Parsons Project: Ammonia Avenue
Rush: Moving Pictures
Assemblage 23: Defiance or Storm
Alice Cooper: Brutal Planet
Pink Floyd: Dark Side of the Moon
Yeah, Zen Arcade’s the one that’s my favorite the other half of the time. I don’t think it’s a good one to introduce the uninitiated to, though, if only because of “Reoccurring Dreams” (which I do love).
Don’t really know Flogging Molly, but I hope for the Pogues you’d pick Rum, Sodomy & The Lash.