Still, there are mixed results. The younger Bush and his counterpart, Vladimir Putin, cooperated on counterterrorism and agreed to arms cuts but fell out over what Russia regarded as U.S. unilateralism and what the U.S. saw as Russian backsliding on democracy.
Ariel Cohen, a Russia expert at the Heritage Foundation think tank in Washington, said American presidents have "tried to reach out and remake Russia in our image."
Along the way, he added, "we stepped on a lot of toes and broke a lot of china."
During a May appearance in Washington, Russian Foreign Minister Sergey Lavrov complained that the U.S. is encroaching on Russia's security.
He cited the expansion of the North Atlantic Treaty Organization to Russia's borders and U.S. support for the applications of Georgia and Ukraine to join the military alliance. The Kremlin opposes NATO membership for its former Soviet allies.
Lavrov said that if the United States wants to "reset our relations" this year, "then we must get rid of the toxic assets inherited" from last year. That includes the proposed U.S. missile-defense system that would place radar in the Czech Republic and interceptor missiles in Poland, both Russian neighbors.
Michael McFaul, the Russia expert in the Obama White House, told reporters before Obama's trip that the new U.S. president does not intend to give in on NATO or missile defense. McFaul said the U.S. contingent in Russia will not use the term "reassure" on either topic.
"We're going to define our national interests," McFaul said. "And then we're going to see if there are ways that we can have Russia cooperate on those things."
A look at highlights, challenges of past summits
President Obama arrives in Moscow today at the invitation of his Russian counterpart, Dmitry Medvedev. Obama has said he wants to "reset" the frayed relationship between the United States and Russia, which has challenged leaders of both countries for years. USA TODAY's David Jackson reviews some noted meetings.