At best, the man will be remembered as one of the most incompetent president's ever. For the sake of argument, I'm going to say he was a man of integrity and a good, well-intentioned man. So he was met with terrible circumstances: 9/11 and the war on terror.
However, he was so incredibly poor at it. The war ruined the economy but America into a huge deficit, failed to stop Al-Qaeda or even get Osama Bin Laden, entered a bizarrely irrelevant war to the war on terror, and destabilised the Middle East.
But more likely, he will be remembered as one of the most incompetent and most corrupt Presidents in history. He treated the US economy as an ATM for his Wall Street friends - and left New Orleans in ruins after a hurricane. Cheney, Rumsfeld, and the rest will be remembered, even by the right wing given time, as a terrible president who was so awful, the country became hated abroad and became so desperate for change from his failure as president, that the first black man got elected as president. And that little shining light (unless Obama turns out to be even worse) will be the only nice thing anyone can say about the administration.
And if we're lucky, they'll get impeached for some of the **** they pulled and end up in prison.