With thousands of heavily armed Russian troops occupying this perennially embattled peninsula, an overwhelming majority of Crimeans voted on Sunday to secede from Ukraine and join Russia, resolutely carrying out a public referendum that Western leaders had declared illegal and vowed to punish with economic sanctions. The outcome, in a region that shares a language and centuries of history with Russia, was a foregone conclusion even before exit polls showed more than 93 percent of voters favoring secession. Still, the result deepened the conflict over Ukraine, forcing the United States and its European allies to decide how swiftly and forcefully to levy threatened sanctions against Russian officials including top aides to President Vladimir V. Putin.