The Democratic president promised "smarter" rather than bigger government for "the many, and not just the few".
He also called for action on gun violence, climate change and immigration reform.
In the Republican response, Senator Marco Rubio urged Mr Obama to drop his "obsession" with raising taxes.
Speaking in the House of Representatives, Mr Obama told his audience that his generation's task was "to reignite the true engine of America's economic growth - a rising, thriving middle class".'North Star'
"We have cleared away the rubble of crisis, and we can say with renewed confidence that the state of our union is strong,'' Mr Obama said in an hour-long address.
Delivering growth and jobs will be the "North Star that guides our efforts", he added.
Those hoping for a more conciliatory tone than this notably aggressive State of the Union speech were disappointed”
But he insisted that nothing he planned would raise the deficit "by a single dime".
Mr Obama proposed reforms to reduce the cost of Medicare, a federal healthcare programme for pensioners, but argued "we can't just cut our way to prosperity".
In his speech, Mr Obama went on to call for federal investment in infrastructure, clean energy and education.
And he vowed to act on climate change himself if Congress failed to enact legislation.
"I urge this Congress to pursue a bipartisan, market-based solution to climate change...," he said.
"But if Congress won't act sooner to protect future generations, I will. I will direct my cabinet to come up with executive actions we can take, now and in the future, to reduce pollution, prepare our communities for the consequences of climate change, and speed the transition to more sustainable sources of energy."
Mr Obama also said he would reduce by more than half the number of US troops in Afghanistan over the next year.
Watch President Obama's full address
He asked Congress to raise the minimum wage, called for legislation to ensure women are paid equally to men, and announced a commission to improve the voting process.
On gun control, Mr Obama said an "overwhelming" majority of Americans supported "common-sense reform" on firearms, including tighter background checks and restrictions on "weapons of war and massive ammunition magazines".
And he urged gun-control opponents to allow a vote in Congress on his proposals.
"The families of Oak Creek, and Tucson, and Blacksburg, and the countless other communities ripped open by gun violence - they deserve a simple vote," he said.Conservative divisions
He also praised bipartisan efforts to draw up an immigration reform bill, adding that if he is sent legislation, "I will sign it right away".
Less than a day after North Korea tested a nuclear device, Mr Obama said the US will "lead the world in taking firm action in response to these threats".
Mr Obama will take to the road in the coming days to push his economic recovery proposals, stopping in the US states of North Carolina and Georgia and in his hometown of Chicago, Illinois.
Republican Senator Rubio: 'I hope the president will abandon his obsession with raising taxes'
Sen Rubio, a possible 2016 Republican presidential candidate, delivered his party's official riposte.
In it, he attacked Mr Obama's economic policies and said "more government isn't going to help you get ahead, it's going to hold you back".
The Cuban-American senator, who also made his address in Spanish, referred to the pain felt by residents of the working-class neighbourhood in which he grew up.
He told Mr Obama: "I don't oppose your plans because I want to protect the rich. I oppose your plans because I want to protect my neighbours."
The Florida senator also warned the president that the "tax increases and the deficit spending you propose will hurt middle-class families".
Underscoring conservative divisions, immediately after the Rubio speech Kentucky Republican Senator Rand Paul delivered the Tea Party's rebuttal to Mr Obama's address.
He said both parties had failed voters by driving up trillion-dollar deficits.
