Seven Mary Three
3 (Keith Emerson, Robert Berry & Carl Palmer, 1988)
Tommy Tutone (okay, maybe not)
Zebra
Huffamoose
Fishbone
Sopwith Camel
Frampton’s Camel
Leftover Salmon
Automatic Man (what, you don’t consider Man an animal?)
And if you count The Animals, you have to count Animal Logic
Frogwings
D’oh!
How could I forget…
The Cowsills!
And Seals and Croft.
Animal Collective
Le Tigre
Danger Mouse
Cat Power
Lamb
Modest Mouse
Tortoise
Wolf Parade
Four Tet
Gang Of Four
Onelinedrawing
Revolting Cocks
Dogs D’Amour
The Bloodhound Gang
are Seal and Skunk Anansie allowed ?
Five for Fighting
Let’s add in a third category – modes of transportation.
I can only think of five.
The Bus Boys
Caravan
The Cars
The GTOs
Train
The Derek Trucks Band 
Cycle Sluts From Hell
Motorhead
Skatemaster Tate (Good lord, did I really just think of Skatemaster Tate?)
Led Zepplin
REO Speedwagon
Wings (maybe?)
Cool.
Led Zeppelin
Wings
Grand Funk Railroad
Jefferson Flightcraft
The Bay City Rollers (as in skates… do I get a ding ding ding?)
You can say that again.
Jefferson Airplane
Jefferson Starship
Sigue Sigue Sputnik
Chicago Transit Authority 
B-52’s
SR-71
Crazy Horse (you didn’t specify mechanical modes of transportation)
Trolley
Joan Jett
The Edsels
Frankie Ford
Mink DeVille (as in Cadillac DeVille)
Flash Cadillac and the Continental Kids
U2 (the spy plane)
Love and Rockets
Flying Machine
The Jets
ANIMALS:
The Penguins (“Earth Angel”)
The Blackbyrds (“Walking in Rhythm”)
The Falcons (“You’re So Fine”)
The Flamingos (“I Only Have Eyes for You”)
The Larks (“The Jerk”)
The Swallows (“It Ain’t the Meat [It’s the Motion]”)
The Jayhawks (“Stranded in the Jungle”)
The Cardinals (“The Door Is Still Open”)
The Spaniels (“Goodnight, Sweetheart, Goodnight”)
The Swan Silvertones (gospel group)
Buddy Holly and the Crickets
Buffalo Springfield
Hootie and the Blowfish
Iron Butterfly
The Stone Poneys (“Different Drum”)
The Impalas (“Sorry [I Ran All the Way Home]”)
Crazy Elephant (“Gimme Gimme Good Lovin’”)
Edward Bear (“Last Song”)
The Teddy Bears (“To Know Him Is To Love Him”)
Cat Mother and the All Night News Boys (“Good Old Rock N Roll”)
The Black Crowes
John Cafferty and the Beaver Brown Band (“On the Dark Side”)
Glass Tiger (“Don’t Forget Me When I’m Gone”)
Trout Fishing in America
The Flying Lizards
Exdploding White Mice
The Golden Palominos
Poi Dog Pondering
Jesus Lizard
The Chicago Bears Shufflin’ Crew (“The Super Bowl Shuffle”)
The Human Beinz (“Nobody But Me”)
And in Spanish:
Los Lobos
NUMBERS:
2 Live Crew
2 in a Room (“Wiggle It”)
The Three Degrees (“when Will I See You Again”)
3 Mustaphas 3
Timbuk 3 (“The Future’s So Bright, I Gotta Wear Shades”)
US3 (“Cantaloop [Flip Fantasia]”)
3rd Base
3 Doors Down
Three Days Grace
The Brothers Four (“Greenfield”)
The Four Tops
The Four Seasons
The Four Aces
The Four Lads
The Four Preps
Unit 4+2 (“Concrete and Clay”)
All-4-One (“I Swear”)
4 P.M.
The MC5
Louis Jordan and His Tympani Five
The Five Satins (“In the Still of the Nite”)
The Jive Five (“My True Story”)
"The Five Staristeps (“Ooh Child”)
The Five Man Electric Band (“Signs”)
The Five Keys (“Ling-Ting-Tong”)
We Five (“You Were on My Mind”)
Hi-Five (“I Like the Way [The Kissing Game]”)
Five (“When the Lights Go Out”)
The Click Five
Sixpence None the Richer
The New Colony Six
Eve 6
7 Year Bitch
L7
After 7
S Club 7
The 8th Day (“She’s Not Just Another Woman”)
Finger Eleven
D12
Sum 41
Stars on 45 (“Stars on 45”)
Eiffel 65 (“Blue [Da Ba Dee]”)
95 South (“Woot! There It Is”)
98 Degrees (Nick Lachay’s band)
Apollo 100 (“Joy”)
100 Proof Aged in Soul (“Sombody’s Been Sleeping”)
112
Front 242
Galxie 500
The 1910 Fruitgum Company
And if we include Roman numerals:
Soul II Soul
Big Audio Dynamite II
Boyz II Men
Classics IV (“Spooky” and “Stormy”)
MODES OF TRANSPORTATION
Thin Lizzy
The Fabulous Thunderbirds
The Balloon Farm (“A Question of Temperature”)
Animals:
Caribou
Mouse on Mars
Gorillaz
Mountain Goats
Pedro the Lion
Numbers:
Sevendust
Zero 7
Old 97’s
M83
Half Japanese
From Zero
The 6ths
Transportation:
Train
The Postal Service