Referenced by Stephen Hawking in "A Brief History Of Time". There are three arrows of time: psychological, cosmological, and thermodynamic.
The thermodynamic arrow of time is defined as the direction in which entropy increases. A universe with a thermodynamic arrow of time opposite to our own would become more orderly (i.e., less entropic) with the passage of time. It is postulated that life could not exist in such a universe, as life as we know it is based on the consumption of resources (thus increasing entropy). However, it's possible that our definition of life is simply too narrow.
The psychological arrow of time is the way that we perceive time -- namely, that we remember the past and anticipate the future. It is postulated that the psychological arrow of time must always point in the same direction as the thermodynamic arrow of time, because our consciousness is a direct result of chemical processes in our brain, bound by the Three Laws of Thermodynamics. If in some way this arrow were reversed with respect to the thermodynamic arrow, we would experience time flowing backwards, essentially remembering the future and knowing nothing of the past.
The cosmological arrow of time points in the direction in which the universe is expanding. Some believe that unlike the thermodynamic arrow of time and the psychological arrow of time, this arrow could concievably point in a different direction, particularly if the universe stops expanding at some point and begins contracting in on itself. Others believe that if this were to happen, the other arrows of time would change directions as well: entropy would decrease, and time would run in reverse, though we wouldn't realize it since our minds would also run backwards. Hawking once thought that this would be the case, but has since retracted that belief.
In our universe, all three arrows point in the same direction, which we consider "forward".