Brains don't have nerve terminations, or at least, no touch sensitive ones.
For this reason, it is possible to perform brain surgery with a local anaesthesia. Neurologists frequently use this technique to cure epilepsy patients who don’t react well to standard treatment. The procedure consists of the surgeon sending small electrical impulses into specific regions of the brain to see how it reacts. Once the problematic region is localized, they evaluate to see if it can be safely removed and proceed as needed. It takes an awake patient to perform this operation because he may have to answer specific questions regarding the way his brain reacts to stimuli.
I can only imagine how comfortable it is to have one’s skull opened with some surgical saw…And the noise…
As radlab0 pointed out: During the "smashing the skull open phase" (craniotomy), the patient is actually put asleep to alleviate the creepiness of it all.