Testosterone therapy does have risks. These are the risks posted on WebMD:

Risks of Testosterone Therapy

The common preparations of testosterone replacement have frequent, mild side effects. Testosterone side effects most often include rash, itching, or irritation at the site where the testosterone is applied.

Testosterone replacement so far seems to be generally safe. Experts emphasize that the benefits and risks of long-term testosterone therapy are unknown, because large clinical trials haven't yet been done.

There are a few health conditions that experts believe testosterone therapy can worsen:
•Benign prostatic hypertrophy (BPH): The prostate grows naturally under the stimulation of testosterone. For many men, their prostates grow larger as they age, squeezing the tube carrying urine (urethra). The result is difficulty urinating. This condition, benign prostatic hypertrophy, can be made worse by testosterone therapy.
•Prostate cancer: Testosterone can stimulate prostate cancer to grow. Most experts recommend screening for prostate cancer before starting testosterone replacement. Men with prostate cancer or elevated prostate specific antigen (PSA) should probably avoid testosterone treatment.
•Sleep apnea: This condition can be worsened by testosterone replacement. It may be difficult for a man to detect this himself, but his sleeping partner can often tell. A sleep study (polysomnography) may be needed to make the diagnosis.
•Blood clots: The FDA requires that testosterone replacement products carry a warning about the risk of blood clots in veins. This could increase the risk of deep vein thrombosis and pulmonary embolism , a potentially life threatening clot that occurs in the lungs. Products already carried a warning about the risk of blood clots due to polycythemia, an abnormal rise in the number of red blood cells that sometimes occurs with testosterone treatment. Now the warning is more general to include men who don't have polycythemia.
•Congestive heart failure: Men with severe congestive heart failure should usually not take testosterone replacement, as it can worsen the condition.

It will be years before large clinical trials bring any answers on the long-term benefits and risks of testosterone therapy. As with any medicine, the decision on whether the possible benefits outweigh any risks is up to you and your doctor.

NOTE (added by Unguy): In addition to the above, in some men increased testosterone has led to an increase in violent behavior.