It's been over a decade since I've tended bar, so there are probably tons of new ones I don't know about, but here's some classics:
Tequila Sunrise
Grasshopper
Mai Tai
Mint Julep
Sea Breeze
Bay Breeze
Beachcomber
Sloe Gin Fizz
Gimlet
Madras
Daiquiri
Nightcap
Long Island
Gibson
Brandy Alexander
Butterball
Mimosa
Vermouth
Absinthe
Highball
Tootsie Roll
Creamsicle
Peppermint Patty
Amaretto
Fuzzy Navel (a bit questionable, perhaps!)
Boy pony names?:
Rusty Nail
Bazooka Joe
Mudslide
B-52
Sidecar
Rob Roy
Tom Collins
Rum Runner
Nutty Irishman
Alabama Slammer
Harvey Wallbanger
Greyhound
Dark&Stormy
Kamikaze
Fireball (oops...already been done, but...)
Bonus points for equine-sounding cocktail names:
Moscow Mule
'Mane'hattan