I predict things will turn out as you would expect. The big future questions are of course: 1) Will the economy recover soon enough? 2) Will terrorism wane? 3) Will any unexpected (or looming) problems arise? Of course on all of these issues, Obama could never have complete control over the outcomes. So we should ask, will his policies and leadership help or hurt the outcomes?
For the economy I think a full recovery will take longer than many people would hope. Instead of making our way out of the recession by 2010 I think we will only recover enough for a noticeable, albeit slight, upswing to be seen by 2012 which will be enough to get Obama reelected. I think the stimuli will help but the U.S. will have a huge national debt that will take decades and a determined Congress to cut down at all. Only by 2016 will the U.S. Financial sector have regained its respect in the U.S. and abroad. Under Obama, Congress will grant the SEC more proactive investigatorial powers and this will help some in preventing future crises. It will be at least two decades before the U.S. financial system forgets the lessons that they should have learned in the present crash. Near future U.S. economic booms won't be as boomy as they have been.
I think by 2010 Obama will have reduced Iraq troop deployments by half, and by 2012 there will only be a 1,000 - 4,000 troops deployed there to assist Iraqi troops and protect the U.S. embassy. There will still be insurgent and sectarian fighting but it will have decreased to a tolerable level (from the perspective of U.S. foreign policy). I think the U.S. troops will begin a slow withdrawal from Afghanistan once it becomes apparent that Osama bin Laden has died. At the end of Obama's second term (and after a "surge") there will be around 10,000 U.S. troops in Afghanistan. Successful terrorist acts will continue to decrease in Western countries, though this will be largely due to beefed up security and investigations.
If another large attack on the U.S. is successful, Obama will lead a massive (and unilateral if the Security Council disapproves) attack on the country of origin. However, unlike Iraq or Afghanistan the occupation will be overwhelming but brief. He will not topple the government in it's entirety but will leave some "less evil" political or military faction in charge and once enough terrorists have been killed or captured there will be a swift withdrawal. Only if it is homegrown will there be confusion on which direction to take.
As for unexpected or looming crises, the U.S. won't go to war against Russia or China (even if China invades Taiwan), although the U.S. might retaliate against aggressive foreign military actions with strong but ultimately temporary trade embargoes. Global warming will not destroy the planet during Obama's presidency although there will be continued loss of biodiversity worldwide. The U.S. energy policy will increase in its wind, solar, geothermal, ocean-powered, and nuclear-powered capacities. However, the U.S. will still get squeezed by high fossil fuel costs once the country gets out of the recession.
Obama will spearhead at least one military intervention in Africa possibly in Zimbabwe or elsewhere due to genocide. There will be several natural disasters to strike the U.S. during the Obama presidency, and Obama will make sure that he is seen to be doing something about them. Several countries will acquire nuclear weapons during the Obama presidency. His response will follow what Bush did with North Korea - bargain for the cessation of the further production of nuclear weapons in return for more foreign aid, thus giving them a trump card but preventing massive arms races. No nuclear weapons will not be used in war during the Obama presidency. An informal "in kind" retaliation doctrine will prevent mini-nuclear states from using their nuclear weapons (aka if Iran nukes Iraq or anyone then the U.S. will nuke Iran). Obama will not be assassinated but at least one would-be assassin with a bomb or a gun will be stopped by the Secret Service.
Obama's presidency will ease some racial tensions, but there will still be racist actions and attitudes in the U.S., both real and perceived. Some poor black Americans will try harder to succeed, but there will still be plenty of gangs, drugs, crime, and poverty among poor black people. I give Obama only a 50% chance of getting truly universal health care legislation passed, and if it does only a 50% chance of it not being screwed up when it starts. Social Security will remain unchanged except for reduced benefits to wealthier seniors and an older retirement age. By the end of his first 6 months in office there will be plenty of Democrats upset that he hasn't changed things more and plenty of Republicans upset at what he has changed - the Democrats, however, will look back at his presidency with fond nostalgia no matter how much consternation he gives them during it.