Yes, he can, but only with certain weapons. When Mels regenerates into River Song, she is shot several times with Earth bullets, which had no effect on her ("Let's Kill Hitler"). However, when the Doctor is "killed" at Lake Silencio, he begins to regenerate, but then River shoots him again with a laser gun, killing him "permanently" ("The Wedding of River Song"). However, it should be noted that that regeneration was fake, as it was actually the Tesselecta, and the real 11th Doctor had no regenerations left. "Turn Left" suggests that drowning could have killed the Doctor had Donna not rescued him.