The roots of the teeth may be long or short. Having long roots is an advantage; it allows the tooth to be securely embedded in the jaw bone while tearing food. This enables the tooth to better resist lateral forces in mastication. You will notice that the canine teeth have the longest roots; canines (also called cuspids) are used for tearing tough foods, when heavy lateral forces are applied.
Having short roots is a disadvantage. If there is gum recession, or loss of bone due to gum disease, then the teeth will have less support, leading to wobbly teeth. Teeth with shorter roots are more likely to get knocked out of position in accidents, for example in sports.
Teeth with long roots are more difficult to extract. If you have a tooth that needed extraction, (such as a wisdom tooth) you would wish the root/roots was shorter.
Teeth with long roots are more resistant to orthodontic tooth movement. If you want quicker orthodontic treatment, you would need to have shorter roots.
See also: Wisdom tooth