Pop - Madonna, Michael Jackson, Prince
Rock - Fleetwood Mac, The Beatles, Rolling Stones, Sly & The Family Stone, Springsteen
Soul - Marvin gaye, Aretha Franklin, Etta James
Alternative - Kate Bush, grace jones, Bjork, The Velvet Underground/Nico
R&B - Janet Jackson, Diana Ross, Whitney, Mimi Carey, MJ, Prince
Hip-Hop/Rap - Notorious b.i.g, Lauryn Hill, Aaliyah, TLC
Country - Dolly Parton
Dance - Madonna, The Prodigy, Donna Summer, Kylie Minogue, Janet Jackson
Classical - Mozart, Beethovan, Bach

They who rule the roost

Pop - Michael Jackson
Rock - Queen
R&B - Usher
Hip-Hop/Rap - Eminem
Country - Johnny Cash
Dance - Kraftwerk/Daft Punk
Classical - Pavarotti (if you want to bracket Opera with Classical)

and throwing a new one in there

Metal - Metallica

Great thread idea, really difficult to choose in some of the categories. My own choices would be:

Pop - Michael Jackson or Madonna, Queen (who could also go into the Rock category)
Rock - problem here, if it's rock and roll then Elvis or Buddy Holly. If it's rock music then it would be The Rolling Stones, The Beatles or possibly The Who
Soul - James Brown, Aretha Franklin
Alternative - define alternative? Pink Floyd as they don't really fit into mainstream rock/pop although they've had hits in those genres. Otherwise I'd put someone like The Smiths in here.
R&B - traditional R & B, anything that came out of Motown, modern R&B no idea I can't do doing with it but I guess Beyonce would go here
Hip-Hop/Rap - Run DMC, Beastie Boys
Country - Dolly Parton or Johnny Cash
Dance - Fatboy Slim,
Classical - Beethoven

I'd also add in

Metal - Black Sabbath, Rainbow, AC/DC
Glam Rock - KISS, Slade, Wizzard
Goth - Sisters of Mercy, The Damned, The Cult
Punk - Bauhaus, The Sex Pistols, Dead Kennedys
Folk - Fairport Convention, Steeleye Span, The Albion Band, Pentangle
Jazz - Billie Holiday, Ella Fitzgerald, Louis Armstrong, Bix Beiderbeck
Blues - Muddy Waters, Van Morrison (crossover into folk)
All-round Entertainer - Frank Sinatra

ETA: I've tried to stick to one or two at the most but could easily have included loads more in each category that I think are/were the greatest. I've also tried to be objective and not pick my favourites.

Today's modern "stars", I don't think there's many who will still be on the shop shelves and promoted as any of the "greats" of these genres still are, many 40 or 50 years later.

Hiphop group has to be Public Enemy

Country --> Loretta Lynn, Dolly Parton, Patsy Cline, Kitty Wells

Pop - beatles
Rock - led zep
Soul - otis redding
Alternative - smiths
R&B - usher?
Hip-Hop/Rap - snoop
Country - johnny cash
Dance - ferry corsten
Classical - any...dont think ones bigger then others out of the main contenders

good call there... esp emboldend

Pop: Kylie Minogue or Madonna
Rock: David Bowie
Soul: Dionne Warwick
Alternative: Grace Jones
R&B: Prince or Diana Ross
Country: Dolly Parton or Kenny Rogers
Dance: Janet Jackson

my choices are - : (not sure about a couple though)

Pop - Madonna, Michael jackson, Abba, BeeGees, Celine Dion,

Rock - Led Zeppelin,Tina Turner

Soul - Prince, Aretha Franklin, Dusty Springfield, Marvin Gaye, Lionel Richie, Barry White

Alternative - U2, Moby, Oasis, Enya

R&B - Janet Jackson,Luther Vandross,Boyz 2 Men, Patti LaBelle, Diana Ross, The Fugees, Mariah Carey, Chaka Khan

Hip-Hop/Rap - Dr Dre, Missy Elliott (best female hip hop artist)

Country - Dolly Parton, kenny rogers

Dance/Trance - Tiesto, Paul Oakendold, Armin Van Buuren, ferry corsten

Reggae - Bob Marley, Lauren Hill

Jazz,Gospel, Folk - Ella Fitzgerald, Frank Sinatra, Eva Cassidy,

Far too difficult to answer. Are Beatles Pop? They weren't really post 65. They were more pre-prog...
Same with Pink Floyd. Brilliant band, but where do you put them? Rock? Led Zep would probably win Rock, but too many others that don't quite fit niches.

Soul's easier, James Brown probably, but what about Aretha and Marvin Gaye? Stevie Wonder?
Classical? Probably Beethoven. But what about Bach and Mozart?

Too many choices. Can't decide.

I'm just gonna do the genres I'm most interested in:

Pop: Michael Jackson
Rock: Queen
Soul: Stevie Wonder
Alternative: The Cure

A few others:
New Wave - New Order
Punk - The Clash
Metal - Metallica

cant dance be in the same category as pop. dance-pop.

pop has several names like dance-pop, electro-pop, country pop, synth-pop, urban pop (r&b and pop together)

here are a few artists' primary genres:

michael jackson-pop, r&B, soul, rock, disco
madonna: pop
janet jackson: pop, r&b
whitney houston-pop, soul, r&B, gospel
mariah carey-pop, soul, hip hop, r&b
celine dion-pop
britney spears-pop
beyonce-r&b, hip hop, soul, pop
rihanna-pop, r&b, hip hop, reggage
lady gaga-pop
katy perry-pop, rock
selena-tejano, latin pop, pop, r&b
aaliyah-r&B, hip hop, soul, pop
adele-soul
avril lavigne-pop, rock
alanis morissette-rock, pop
alicia keys-r&b, soul
ashanti-r&b, hip hop
black-eyed peas-hip hop, r&b, pop
brandy-r&b, hip hop
bruno mars-pop
carrie underwood-country, country pop
cher-pop, rock, disco
chris brown-r&b, hip hop, pop
christina aguilera-pop, r&b, soul, latin pop
destiny's child-r&B, hip hop, soul
en vogue-r&b
faith evans-hip hop, soul, r&b
faith hill-country pop, country, pop
fergie-pop, r&b, hip hop
fey-latin pop
fugees-hip hop
gloria estefan-latin pop, pop
grupo limite-latin pop, tejano
gwen stefani-pop, rock, r&b
hilary duff-pop
jennifer hudson-r&b, soul
jennifer lopez-pop, latin pop, r&b
jordin sparks-r&b, pop
justin timberlake-pop, r&b
lady antebellum-country, country pop
las ketchup (one-hit wonder)-latin pop
lauryn hill-r&b, hip hop, soul, reggage
leann rimes-country pop, pop, country
lee ann womack-country, country pop
leona lewis-pop, r&b
mary j blige-hip hop, soul, r&b
miley cyrus-pop
natasha bedingfield-pop
no doubt-rock, pop, r&b
noeila-latin pop
nsync-pop, r&b
p!nk-pop, rock, r&b
paula abdul-pop
paulina rubio-latin pop
salt n pepa-hip hop, r&b
shakira-latin pop, pop, rock
shania twain-pop, country pop, country
sheryl crow-rock, pop, country
sinead o connor-rock
taylor dayne-pop
taylor swift-country pop, pop, country
thalia-latin pop, pop
tlc-r&b, hip hop, soul, pop
toni braxton-r&b, soul, pop
usher-r&b, soul, pop
vanessa williams-r&b, soul
vanessa carlton-pop

these artists i listen to and to name a few

yes...its only because 50 years later the definition has shifted somewhat over what pop is.. anyway, most of sg peppers is pop (67) and theres awful tracks like ob-la-de ob-la da... mixing simplistic pop tracks with other more creative tracks doesnt really alter their pop credentials.

are beatles pop? yes

http://en.wikipedia.org/wiki/Pop_music

are pink floyd rock? yes. prog was short for progressive rock

http://en.wikipedia.org/wiki/Rock_music

all those artists you mentioned are soul. james was the godfather of soul and aretha was the queen of soul

http://en.wikipedia.org/wiki/Soul_music

and bach, mozart and beethoven are all classical

http://en.wikipedia.org/wiki/Classical_music

Yep, I wouldn't actually say that the Beatles were a 'rock' band. They were never heavily guitar led.

'Rock' evolves from the R+B British bands of the 60s, like The Stones and Who, and probably more directly from the Yard Birds which had Clapton, Beck and Page in them. Then link in American influences from Hendrix etc.

The problem with 'Pop' is that it evolves from whatever is the main musical influences of the time, from Rock, or Disco, or Dance, or urban music etc.

tbh i never 'got' why the beatles are/were refered to as 'rock'.. even dave dee dozy beaky mick and tich had 'heavier' tracks...'hold tight' for eg... and they were firmly pop.

Pop - ABBA
Rock - Queen
Soul - Aretha Franklin
Alternative - Smiths
R&B - James Brown
Hip-Hop/Rap - pass
Country - Garth Brooks
Dance - Michael Jackson
Classical - Beethoven

Missed one out so I'll add ...

Folk - Bob Dylan

Electronic = Gary Numan, Kraftwerk, Human League

I'd like to see you telling Jeff Mills that he makes pop music.

Lol alternative

Pop is Madonna and Michael Jackson.

Country is obviously Dolly Parton.

Missed Electronic. I would have voted, like you, Kraftwerk.

What would you choose for these genres ...

Blues
Jazz
Latin
Lounge
Chilled