Using a tanning bed, booth, or sunlamp to get tan is called indoor tanning.  It is very well-known that exposure to ultraviolet (UV) rays from indoor tanning can cause skin cancers including basal cell carcinoma, squamous cell carcinoma, and melanoma, which is the deadliest type of skin cancer.  
In addition to causing cancer, UV exposure can also cause damage to the eye including cataracts and cancers of the eye such as ocular melanoma.  Both the International International Agency for Research on Cancer (part of the World Health Organization) and the U.S. Department of Health and Human Services classify indoor tanning as a human carcinogen, or something known to cause cancers in humans.  The CDC (Centers for Disease Control and Prevention) has numerous warnings about indoor tanning, and the American Academy of Dermatology has a very strong position statement against indoor tanning.  

Dangers of Indoor Tanning
Indoor tanning exposes users to two types of UV rays, UVA and UVB, which damage the skin and can lead to cancer. Indoor tanning is particularly dangerous for younger users; people who begin indoor tanning during adolescence or early adulthood have a higher risk of getting melanoma. This may be due to greater use of indoor tanning among those who begin tanning at earlier ages.Every time you tan you increase your risk of getting skin cancer, including melanoma. 

Premature Aging
In addition to skin cancer, indoor tanning causes premature skin aging (wrinkles, age spots), changes the texture of the skin, and can increase the risk of potentially blinding eye diseases if eye protection is not used.

The Bottom Line
In short, just don't do it!  People always comment that dermatologists have great skin.  What is the secret?  It is that we never tan!  Embrace your pale, follow these tips for sun protection, and your skin will thank you for it.  

Learn more about skin cancer:
Basal cell carcinoma
Squamous cell carcinoma
Treatment of skin cancer
Skin examinations