In the early 1930s, Adolf Hitler promised "change." The Germans did, indeed, get change. In the 2008 Democratic Campaign was based upon the word change. What might have happened if people had knowledge of the previous usage of this word?
All the above posts cast interesting and truthful views as to the importance of history.
I'd like to add that a knowledge of history informs the present. Regardless of whether we can learn from past mistakes, since man is said to be the only animal who stumbles twice on the same stone, history helps us understand the world in which we live "as is."
If we take an active interest in evolution, many of the things we take for granted will acquire a new meaning. Some people contend that, as history is past -or so they think- it is also dead.
It would be wise to conceive of history both synchronically and diachronically. A synchronic view tells us of what was happening in the world at the same time. This shows us the diffences and similarities among cultures at every step of their development. A diachronic view shows us the links in the chains of events that have led mankind to its present state.
We generally like to know about our family history. In the big picture, History as a discipline explains the whys and wherefores of that extended family we call the human race.
It is important for a culture to know where it's been if it is to make sound decisions as to where it's going. For example, when one looks at the conditions in Europe that made the Holocaust possible, it becomes apparent that the horrors were more than just the mark of a sociopathic egomaniac (Hitler). Although he was the leader who orchestrated the murder of six million Jews and five million others, such a thing might not have been possible if there hadn't already been a racial prejudice toward Jews extending back through history. There was plenty of animosity toward Jews for Hitler to capitalize on, and his ideas were actually not even his own, but based on those of an Austrian named Karl Lueger and his Christian Social Party.
So what does this mean for us? One thing it suggests is that society as a whole, and we as individuals need to be very careful about condoning, or sitting silently by when racial prejudice rears its ugly head. We must also be aware of what our government is doing, and raise our voices when it oversteps its bounds. One of the first things the Nazi party did in consolidating power was to require the "registration" of Jews; law-abiding citizens complied, many of them perhaps hoping that their cooperation and loyalty would be rewarded--which, of course it was not. We need to recognize when someone is discouraging us from thinking independently and/or questioning our patriotism when we don't agree with something or someone. However, we cannot learn these lessons if we don't remember the history behind them, i.e. "those who don't know history are condemned to repeat it."
I agree with the importance of learning from past mistakes, but I would argue that the real importance of history lies in the skills and habits of mind that are part of historical practice. Learning obscure facts about long-dead people is not history. It is the study of the past. History involves thinking critically, and, most importantly, evaluating the actions of past people in their context. This involves a set of critical thinking skills that are not necessarily present in other disciplines.
To really understand another nation and another culture, you have to know something about their history. Look at how little we understand about Middle Eastern cultures--the average American knows nothing about the history of Iraq or or Iran, yet we are in constant conflict in the Middle East. If we understood these cultures better we would probably have better relationships with them.
I have to, once again, support pohnpei's answer. Knowing history is important because it teaches one how not to repeat the mistakes which have been made in the past.
Outside of that, as with literature, history is important so that one can understand the time period the piece is written in. Some students may not understand a piece of literature unless they know the historical setting it was placed in.
We would be more likely to make mistakes. I think that we do actually learn something from our mistakes. Maybe we don't learn those lessons well enough at times, but I think that we do learn. If we knew nothing about the past, we could keep on making the same mistakes over and over again.