The Beastie Boys are a rap group?
I don't know that I can really narrow it down to one album per genre. Here are some of my favorite albums by genre (at least in the way I would classify them).
Female Vocal:
Norah Jones - Come Away With Me
Norah Jones - Feels Like Home
Sheyrl Crow - The Very Best of Sheryl Crow
Sade - Best of Sade
Sarah McLachlan - Mirrorball
Charlotte Church - Enchantment
Jewel - Spirit
Male Vocal:
Josh Groban - Closer
Josh Groban - Josh Groban
Boyz II Men - II
The Nylons - Perfect Fit
Az Yet - Az Yet
The Rat Pack - Live at the Villa Venice
Rock (all types) :
Collective Soul - Hints Allegations and Things Left Unsaid
Cowboy Junkies - One Sould Now
Live - The Distance To Here
Live - Throwing Copper
Nirvana - Nevermind
Pearl Jam - Ten
Alanis Morrisette - Jagged Little Pill
Stabbing Westward - Darkest Days
Prodigy - Fat of the Land
Spin Doctors - Pocket Full of Kryptonite
Linkin Park - Hybrid Theory
Linkin Park - Meteora
Evanescence - Fallen
Santana - Supernatural
Santana - Shaman
Mandy Moore - Coverage (not really sure where else to put this one, it's certainly not pop or r&b)
Matchbox Twenty - Mad Season
Country:
Garth Brooks - Fresh Horses
Garth Brooks - The Hits
Trisha Yearwood - Songbook
Martina McBride - Greatest Hits
Deana Carter - Did I Shave My Legs For This
Lee Ann Womack - I Hope You Dance
Dixie Chicks - Fly
Jazz:
Diana Krall - The Girl in the Other Room
Diana Krall - When I Look In Your Eyes
R&B:
The Tony Rich Project - Words
Rap:
Eminem - The Eminem Show
Eminem - The Marshall Mathers LP
Eminem - The Slim Shady LP
Bone Thugs-N-Harmony - E. 1999 Eternal
Bone Thugs-N-Harmony - Resurrection
Snoop Doggy Dogg - Doggystyle
Dance/Pop:
Michael Jackson - Dangerous
Britney Spears - In The Zone