There are numerous levels of obedience titles that can earned by dogs through the AKC. Even dogs that aren't registered with the AKC can participate. All their owners need to do is obtain a PAL/ILP number from the AKC through an application if the dog appears to be purebred.
The BHCSC holds obedience competition for basset hounds at it's BHCSC Specialty Shows in March. The information below may help you understand this program. You can also find obedience information on the AKC website.
Basset Hound Obedience