Can you still feel pain under general anesthesia?

Not usually: When you are under general anesthesia, you are rendered unconscious so you will not experience pain.

No: Pain is the conscious perception of a noxious stimuli. Since you are unconscious you cannot "feel" the pain. The nerves will still send information to your brain but you will not be able to process this. This is one of the primary goals of anesthesia.

Yes: General anesthesia essentially makes your brain ignore noxious (painful) stimuli. You still "feel" the pain (the painful stimuli get to the brain), but your brain mostly ignores it . With local anesthesia, the brain does not get the signal, since the anesthetics, simply, block the nerve conduction to the areas of the brain that process pain signals.