"Having come so far and achieved so much, we must not allow this to happen," he said.
The US leader also praised the results of the so-called surge of US troops sent to Iraq last year.
He also welcomed the formation of the "Awakening Councils," groups of Iraqis who have sided with the US to confront al-Qaeda in Iraq.
"Al-Qaeda is on the run in Iraq and this enemy will be defeated.''
The US president also stepped up his rhetoric against Iran, warning Tehran that the US will confront any threats against its forces.
"America will confront those who threaten our troops, we will stand by our allies, and we will defend our vital interests in the Persian Gulf."
His comments come less than a month after the Pentagon claimed that Iranian speed boats aggressively approached US Navy patrols in the strategic Strait of Hormuz.
Bush urged congress to pass his $150bn economic stimulus plan "as soon as possible".
To raucous applause, the US leader also urged legislators to pass a bill making tax cuts permanent.
The US president also urged congress to pass free-trade deals with Colombia, Panama and South Korea.
Democrats have opposed the deal with Colombia over its record on human rights and trade union organisation.
Bush's seventh State of the Union speech was a chance to set the tone for his final months in office and try to salvage his legacy before he leaves office in January 2009.
Ahead of Tuesday's Republican presidential contest in Florida, the US leader could struggle to gain attention amid the 2008 election campaign.
Marwan Bishara, Al Jazeera's senior political analyst, said the speech offered little that was new in terms of policy.
"In many ways Bush returned to the same themes, addressing them in the same old way, as if nothing had happened over the last six years."
Dennis Kucinich, the Democratic senator for Ohio who recently withdrew from the race for the presidential nomination, said he was "troubled" by foreign policy aspects of the speech.
"He seems to want to continue the war in Iraq and ramp up for a war in Iran."
"The president continues to misread the Middle East and this is a great problem for peace."
The US leader also spoke at length about domestic issues, including immigration and stem-cell research.