Theoretically, if one were to experience time flowing backwards, it would be due to one's psychological arrow of time pointing in the opposite direction of the thermodynamic arrow of time. Such a person would see a reversal of cause and effect; for example, shards of glass would assemble themselves into a window when a ball flew through it. Pregnancy would be the cause of sex rather than the other way around.
Some music videos (such as that from "Return to Innocence" by Enigma) have incorporated video played in reverse to illustrate this concept. Arguably, there is a sort of odd peace in the idea of the universe becoming more orderly as time goes on, instead of the other way around.
In some myths, Merlin is said to have lived his life backwards: he remembers the future and forgets the past. Naturally, the ability to do so opens the door for all sorts of temporal paradoxes.