- In folk speech one can give three cheers for someone, but not two or four. (And each cheer may consist of "Hip, Hip, Hooray.")
- The starter for a race will say "One, two, three, go." He will not count to two or four. (Cf. the three commands "On your mark, get set, go.)
- The alphabet is referred to as the ABC's; one does not speak of learning his AB's or his ABCD's.
- In jokes, there are commonly three principals: a minister, a priest, and a rabbi; or a blonde, a brunette, and a redhead.
- In horse racing the three possibilities are win, place, and show. In many American games there is more than the binary possibility of winning or losing. The third alternative, that is, drawing or tying, allows the choices win, lose, or draw.
I agree that 3 is important. I would put it way up there. Not above 2, but before 4.