When getting your wisdom teeth extracted, is it necessary to be totally unconscious?

Absolutely not: It should be a joint decision between you and your oral surgeon. If you prefer it then you should make it known that you prefer that it be done with conscious sedation or local anesthesia.

No: Many dental practices routinely "put you to sleep". Some practices are set up that way and don't think to give you an option. Many give the option. Many practices, mine included, never put patients to sleep. Some teeth are so badly impacted that the patient should be "knocked out" so they don't have to deal with the sounds or pressure. Discuss these options with your dentist.