As an experienced Auror, who has lost an eye, leg, and part of his nose while fighting the Dark Arts, Moody is cautious, and refuses to eat or drink anything which he himself has not prepared.
In Harry Potter and the Goblet of Fire, he was locked up in a chest while Barty Crouch Jr, a follower of Voldemort, used the Polyjuice Potion to take his form, and, so disguised, his place teaching Defence Against the Dark Arts at Hogwarts. Moody owes his life to the fact that one ingredient of the Polyjuice Potion is a part of the person whose form is to be assumed, such as a tuft of hair. Moody's habit of carrying his own drink allowed Crouch to take the Potion regularly without raising suspicion. Moody is particularly conspicuous because of his peculiar magical eye which is capable of visually penetrating through most surfaces, and which can rotate through 360 degrees (hence the nickname "Mad Eye").