All anesthetics (regional, general, and even simple sedation) carry some degree of risk. The likelihood of a given complication is usually dictated by the anesthetic technique, type of surgery, and other medical problems you may have (including obesity, smoking, and drug use).
With modern anesthetic techniques, however, the chance of a serious complication is exceedingly rare. Your anesthesiologist will recommend the type of anesthetic he/she feels is most appropriate for your surgery, provide you the best postoperative pain control, and minimize your risk.
The risks that apply to all regional anesthetic techniques are local anesthetic toxicity (seizures, unconsciousness, and cardiac rhythm abnormality with cardiac collapse), soreness at the injection site, bleeding/hematoma/bruising at the injection site, nerve damage, and an incomplete or failed block. Again, the risk of any of these complications occurring is very low, but never zero. Specific complications and side-effect risks are best discussed with your anesthesiologist.
The vast majority of patients undergo regional anesthesia with few if any side effects. However, the notion of nerve damage, regardless of how unlikely, frightens many people. Nerve injuries have been reported after all types of anesthetics, both regional and general. The reported frequency of this complication, depending on how it is defined, ranges from essentially zero to as high as 10 percent.
The good news is that nearly all of the "nerve injuries" are either very short-lived (days) or simply go away (heal) on their own, leaving no residual difficulty. While mild nerve dysfunction is a relatively common issue after all types of anesthetics, it is incredibly rare for a patient to have a permanent nerve injury after any kind of anesthetic.