General anaesthesia has been around for more than a century, and is very safe overall, even for patients who have significant health conditions.
Although some people may think of it as simply falling asleep, for others, the idea of "going under" is a deep anxiety-provoking factor when surgery has to be performed. And the premise of the 2007 thriller Awake might scare the wits out of many people who need major surgery.
In rare cases, patients remain aware under general anaesthesia and they are able to respond to outside stimuli, such as pain, but they cannot recall what happened afterwards. This is known as "connected consciousness".