OK. As per the OP I am to be banished to a desert island and can take the works of a handful of people (which I assume means 5 ):
The complete works of Ella Fitzgerald
The complete works of Frank Sinatra
The complete works of the Gypsy Kings
The complete works of the Beatles
The complete works of Neutral Milk Hotel or the complete works of the Decemberists
Sting, for his occasionally incredibly well written lyrics. Of course, he has a lot of clunkers too, but when he hits, he hits out of the park.
Rush, again for the lyrics.
U2, for producing a very large number of songs I could listen to over and over, despite also producing a lot of songs that I loathe.
Boston, for the music rather than the lyrics, although they produced some good lyrics occasionally as well.
They are a fantastic live band, with plenty of archived shows available. If, on the off chance, you haven’t heard them live, you should definitely check them out. NPR has a few on the All Songs Considered podcast.
I thought I was the only Trip Shakespeare fan around here. I have worn out multiple tape copies of both Lulu and Across the Universe. Never got to see them live, though.
As much as I love In The Aeroplane Over The Sea, I’ve never been able to get into any of NMH’s other albums. Not sure why - it’s not for lack of effort.
Mine:
Rush
Def Leppard
Metallica
Nine Inch Nails
ZZ Top
Johnny Cash
“Weird” Al Yankovic
The Beatles
The Clash, The Jam, The Smiths, The Who, Prince, Pink Floyd
Fun for the whole family there I think.
I could have written this post nearly word for word, though for me it was Echoand the Bunnymen instead of Go-Betweens
There are two bands which, in my opinion, had the kind of magic which can never be duplicated. Van Halen (With Roth) 78-84, and the original Guns & Roses. I almost felt that way about Skid Row, but it’s only their first album that was really great.
Most of my other favorites are a whose who of top 40.
Bob Dylan
Johnny Cash
Nellie McKay
Rufus Wainwright
Alanis Morissette
Goldfrapp
Incredible String Band
Martha Wainwright
Beach Boys/Brian Wilson
Tomoko Kawase, all 3 of her projects - the brilliant green, Tommy february[sup]6[/sup] and Tommy heavenly[sup]6[/sup]. Wonderful voice. Interesting lyrics (when they’re in English). Nice musical aspects (though that part owes more to her husband, Okuda, not Tommy herself). Lots of variety of style, and a pretty good quantity of output, so no matter my mood, I can find a Tommy song I want to listen to.
The Beatles. … For pretty much the same reasons as the above.
Boochy, boochy, boochy, boochy, boochy, boochy, boochy
Squidly, squidly, squidly, squidly, squidly, squidly, squidly
Sham sham shadoo, oh sham sham shadoo
I. Am. Not. Aloooooone. 
Most played at my house over the last twenty-five years or so: Black Sabbath.
I always wondered if that screen name was a “Big Ted” reference.
Pink Floyd
The Beatles
Steve Vai
Hendrix
Joe Satriani
The Who
1990 and prior Metallica
Nirvana
Soundgarden
Alice In Chains
Pearl Jam
U2
Guns and Roses
NIN
Black Sabbath and early Ozzy Osbourne
That’ll do.
Jethro Tull
Pink Floyd
Suzanne Vega
Sinéad O’Connor
Weird Al Yankovic
I could go a long time listening to nothing but those five.
Make sure you do they are great. I was at this gig. Hopefully Moshcam works overseas. It streams an awesome collection of entire recent Australian gigs by a wide variety of artists.
Grateful Dead
Van Morrison
The Meters
Neil Young
Bob Dylan
The Band
Talking Heads
The Who
The Police
Elvis Costello
Los Lobos
The Neville Brothers
Little Feat
(the single most important thing these musicians all really share in common is a love of language and a penchant towards intelligent, insightful lyrics)
These, plus:
The complete works of Nat “King” Cole
The complete works of Simon & Garfunkel
The complete works of Johnny Mathis
The complete works of Barbra Streisand
The complete works of Tony Bennett
The complete works of theGershwins
The complete works of Cole Porter
The complete works of Stephen Sondheim
And
The complete works of Bach, Mozart, Beethoven, Schubert, Mendelssohn, Chopin, Brahms, Tchaikovsky, Verdi, Sousa, Puccini, Scriabin and (especially) Rachmaninoff.
Number one:
The Beatles
My Holy Trinity of singer/songwriters:
Bob Dylan
Neil Young
Paul Simon
Sentimental favorite:
Elvis Costello
Honorable mentions:
Warren Zevon
Townes Van Zandt
John Prine
Hank Williams
Joni Mitchell
Richard Thompson
John Lennon
James Taylor
(early) Lou Reed
Jethro Tull
Gaining in popularity:
Eminem
mmm
Kate Bush
Hoagy Carmichael
Hooverphonic
Bing Crosby
Radiohead
The Gershwins
Gary Numan
Richard Thompson
Drive-by Truckers
Nick Lowe
Leonard Cohen
Okkervil River
The Whitlams
Metallica
Pearl Jam
Alison Krauss
The Mavericks
ETA: make it a top 10 list