Most patients are surprised to hear that they can have procedures under local anesthetic. Many plastic surgeons that perform a high volume of office based surgery will offer this option as an alternative to general anesthesia. I find that many patients, even those undergoing bigger procedures will consider local anesthetic over general because they are more worried about going to sleep. In my practice I combine local anesthetic with oral sedation. The local anesthetic numbs the area so that during the procedure the patient doesn't feel anything. The oral sedative relaxes the patient and eliminates  anxiety so that the patient is not anticipating that something is going to happen. . Probably the best explanation about the effects of oral sedation from a patients perspective is the following quote from a patient of mine that was undergoing an eyelid lift in my office; "I know what you are doing but I don't feel anything and I don't care."
If you are afraid of needles or terrified by the idea of knowing what is going on during a procedure, then you are probably not a good candidate for local anesthetic. In this case I always offer the option to have the procedure at a surgery center with general anesthesia.