There are 23 different breeds of hounds accepted by the American Kennel Club, and numerous others not yet accepted.  The breeds are evenly split between Scent Hounds and Sight Hounds.  Now, this is not to say that scent hounds never chase something they see, or that sight hounds never put their head down and follow a trail, but as a general rule they have two totally different methods of hunting.
 
Scent Hounds The breeds whose primary method of hunting is to follow a trail.  Probably the best known of this group is the Bloodhound and the Beagle.  Click on the individual breed name for more information and  links to the parent club, local clubs and breeders.
 
American Foxhound Bloodhound Norwegian Elkhound
Bassett Hound Dachshund Otterhound
Beagle English Foxhound Petit Basset Griffon Vendeen
Black & Tan Coonhound Harrier Plott Hound
 
Sight Hounds The breeds whose primary method of hunting is to chase down their prey, by sight.  Probably the best know of this group would be the Greyhound.  Click on the individual breed name for more information and  links to the parent club, local clubs and breeders.
 
Afghan Hound Ibizan Hound Saluki
Basenji Irish Wolfhound Scottish Deerhound
Borzoi Pharaoh Hound Whippet
Greyhound Rhodesian Ridgeback