But the KGB veteran Putin, who called the demise of the Soviet Union as the greatest geopolitical tragedy of the 20th century, sees things differently. He pocketed Obama's concessions on missile defense and nuclear arms, and seeks to expand Russia's domain back toward czarist and Soviet dimensions.
Clinton and Bush encouraged the expansion of NATO and the European Union eastward to include former Soviet satellites and the Baltic nations absorbed by the Soviets in the Hitler-Stalin pact.
But the hopes that the appeal of European-style democracy would spread farther east have not been fulfilled.
Ukraine has remained an economic basket case, with a kleptocracy like Russia's but without its oil resources. Politically, it has been closely and bitterly divided between a pro-Russian east and south, and a pro-Western west and north.
The lure of the European example has been diminished by sluggish economic growth and the troubles of the euro. And if Obama has been unwilling to give military aid, European leaders dependent on Russian natural gas and investments have been wary of imposing economic sanctions.
The real danger may lie not in Ukraine but farther west. Obama's dismissal of his red line in Syria and his tepid actions on Ukraine may lead Putin to believe he will not back up other commitments.
Putin says he is protecting Russian minorities in Ukraine; what if he does so in the Baltic republics?
The British historian Christopher Clark, author of "The Sleepwalkers: How Europe Went to War in 1914," warns of "the danger, in trying to avoid conflagration in Ukraine, that Western leaders fail to provide clear signals to Putin."
The West, he says, must show "firmness and clarity in defending the real red lines established by NATO." That means more U.S. and NATO military forces in the Baltics and Poland. And beefing up U.S. and NATO militaries.
Putin's goal may be to dismantle NATO, as he believes NATO dismantled the Soviet Union, which would be the greatest geopolitical tragedy of this century.