Getting to know the breed:  Here are a few personality traits reviewed by:
The American Kennel Club.
Description
A calm pet that enjoys and needs human companionship. Relative to its size, it's the heaviest boned dog of any breed. Its deep, rolling bark can be amusing. This is a serene and well-behaved dog, but if it's spoiled it can become stubborn. Its gentleness makes it great with children.
General Information
Minimum Living Space House With Large or Unlimited Space. Gated Yard Preferred with Shade. 
Hypoallergenic No
Average Food Cost $40 Monthly
Indoor Energy Level Low -From One End Of Couch To Other
Outdoor Exercise Time 20 minutes/day minimum
Trainability Somewhat Selectively Stubborn
Protectiveness Moderately Protective 
Dominance/Submissiveness Balanced
Health
Average Life Expectancy 12 years
Background
Dog Group Hound Group
Country of Origin France
Natural Instincts Hunting by Scent, Pet or Companion
Appearance
Size Medium
Average Minimum Height 13 inches
Average Maximum Height 15 inches
Average Minimum Weight 40 pounds
Average Maximum Weight 60 pounds
Coat Color All Colors
Coat Types Short
Shedding Sheds A Lot 
Grooming Frequency 2 times/wk
Trimming None
Ear Shape Long
Nails Trimmed Monthly

The Basset Hound is a natural hunter and should never be allowed to roam without supervision. But never fear, they're usually headed for the couch rather than a trail.

Because Bassets are pack hunters, they have a good working relationship with other dogs, or camaraderie.

Basset Hounds are very laid back, sociable, and affectionate. As with any pet, interaction with small children should be monitored. Bassets don't like to have their ears pulled - they're long enough.

When there is nothing better to do, bassets like to sleep, frolic,  wander around & sniff, and  typically are not destructive when left alone. They turn on to food, but not necessarily to a scheduled exercise program. Separation anxiety can be confused for misbehavior. Bassets love to be with their owners.  If you find your basset has misbehaved, give him positive attention. Leave the house as if you were still there (ie.. radio playing, tv "Animal Planet") Give your basset a blanket that has your scent.