Getting to know the breed:  Here are a few personality traits reviewed by:
The American Kennel Club.

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
Average Life Expectancy 12 years
Dog Group Hound Group
Country of Origin France
Natural Instincts Hunting by Scent, Pet or Companion
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

Here are a few recognized color variations for Basset Hounds (Click on color to see photos):

(White & Lt. Buff)
Bleu De Gasconge
Tri-Color  Mahogany
Red & White Black & White