I become shaky and irritable, and I have little control over my emotions or thoughts, lashing out at any sign of hostility or going into a brooding state where my only thought is, "Everyone's out to get me". I also don't have a care in the world and will just say whatever's on my mind, regardless of what others think or care (but that's relatively normal for me). Basically, I become my alter-ego, Jerk Man.
Speaking of staying up late, I once stayed up for 25 hours in college weeks before I dropped out. It was the most unpleasant day of my life there; I was frustrated, woozy, depressed, and I was nearly praying to God to take my life so that I wouldn't have to deal with it anymore. I also became a loud-mouthed, stuttering, mumbling maniac. It was a hard time for me, but I somehow stuck through it.
To sum it all up, when I become tired my mind falls into a state of apathy.