In the late 1990s and early 2000s, doctors began wondering if people ever became aware while under anesthesia. They started doing post-operative interviews to find out. Then they took it one step further, and tested whether people could learn under anesthesia. Check out the results.
Awareness During Anesthesia
Awareness during surgery is so terrifying that multiple horror movies have been made about it. It's also the subject of many second-hand stories and urban legends. These days it's rare for such things to happen. Drugs that immobilize a patient during surgery are given only at the beginning of a procedure, as part of the process of knocking the patient out. They wear off, at which point if you are aware\ you can register a complaint. During longer surgeries, it's not uncommon for doctors to monitor a patient's brain activity to check for distress.
But around the late 1990s and early 2000s, doctors got into investigating the anecdotal evidence regarding awareness during anesthesia. Some of this investigation consisted of interviews, both just after surgery and about a week later, during which people described their experiences. Certain interviews are suspect, because they mention extensive attempts to "jog" the person's memory. Interviewing of this kind has gotten a bad reputation, as it has been known to "jog" people's memories about past lives and extensive abuse by nonexistent satanic cults. Still, other interview-based studies found that in as many as 0.13% of procedures, people gain some awareness while under general anesthesia.
Learning While You're Out
Taking it just a bit of a step further, some studies tried to determine if people could take in and retain information while under general anesthesia. The results are encouraging for those who would rather be absolutely unaware of being poked with scalpels than be able to learn French while under the knife.
One experiment involved an odd assortment of tests. Sometimes people were instructed to touch either their ear or their nose while under anesthesia. During a post-operative interview, they touched the suggested body part longer than the part that wasn't suggested, but only by a matter of seconds. Patients were also played tapes of words, all of which had the same first three letters. Later they were shown those letters, and asked to think of words starting with them. They generally picked more words from the list played during the operation than unlisted words. Finally, patients were played a list of nonsense words, either frequently or infrequently, during the operation. Afterwords, they were asked to guess the comparative frequency of the nonsense words. They recognized the words played more frequently than the ones played less frequently, but the frequently-played words were only recognized 62% of the time.
Anything more complicated than single words seems right out of the question. In a study of a group of patients, half of whom were played "The Three Little Pigs" during an operation and half of whom were played "The Wizard of Oz" during an operation, only 49% of the group guessed right.
Overall, it seems that softer tests of "learning" during anesthesia can get mildly positive results. On the other hand, "controlled studies using explicit memory tests" get "uniformly negative results." However much anecdotal evidence for slight awareness during parts of a procedure under general anesthesia, no one is learning anything while they're knocked out.
[Via Awareness During Anesthesia, The Incidence of Awareness During Anesthesia, Human Learning During General Anaesthesia And S2urgery, Auditory Evoked Responses and Learning During General Anesthesia, Learning and Consciousness During General Anesthesia]