Following the normalization of US-Cuban relations in 2009, US President Barack Obama visited Cuba in August, 2010. Obama met with new Cuban President Nicholas Santiago, the first non-Castro to head Cuba in 50 years, and was warmly greeted by the Cuban people in several public appearances.
President Obama was in Cuba with his wife and daughters for three days. They stayed at the US Naval base in Guantanamo, but visited Havana and several other cities. They even swam at the Playa Girón beach that was the site of the failed Bay of Pigs invasion during the Kennedy administration.
During a 2008 campaign speech in Miami, Obama promised to lift restrictions on family visits and remittances by Cuban-Americans seeking to help relatives on the island. He got 35% of the Cuban-American vote in Florida. Cuban-Americans' tough attitude toward their former homeland has gradually eased, in recognition that the hard line accomplished nothing to remove the Castros from power, and had hurt relatives still living in Cuba.
There is a generational divide among Cuban-Americans. Many older people were born in Cuba and came in the 1960s as political refugees in the early years of Fidel Castro's rule. Their American-born children, as well as refugees who came more recently for economic reasons, were more likely to support easing of sanctions.
A general trade embargo had been in effect since the Cold War in 1962. It was imposed after Cuba siezed properties of American people and businesses, particularly United Fruit and ITT.
The embargo was codified into law in 1992 with the stated purpose of "bringing democracy to the Cuban people", and is entitled the Cuban Democracy Act. In 1996 Congress passed the Helms-Burton Act which further restricted US citizens from doing business in or with Cuba, and mandated restrictions on giving public or private assistance to any successor regime in Havana unless and until certain claims against the Cuban government were met.
In 1999, President Bill Clinton expanded the trade embargo even further by ending the practice of foreign subsidiaries of US companies trading with Cuba in dollar amounts totaling more than $700 million a year.
The embargo was one of the few times in history that US citizens were restricted from doing business abroad, and was the most enduring trade embargo in modern history. Despite the existence of the embargo, the US is the seventh largest exporter to Cuba
The US relaxed sanctions during the Clinton administration, only to see relations become tense again in 1996 when Cuba shot down two unarmed planes flown by members of Brothers to the Rescue, a Cuban-exile organization. It was after that incident that the embargo became law rather than longstanding presidential policy.
President George W. Bush backed sanctions in 2004 and 2005 that restricted Cuban-Americans from visiting family on the island more than once every three years, and narrowed the list of family members to whom they can send remittances.
During the Spanish Ameircan War in 1898, Theodore Roosevelt was in Cuba fighting with the "Rough Riders" calvary regiment to help Cuba win indepedence from Spain, but this was before Roosevelt was president. In 2002, Jimmy Carter visited Cuba, but this was after he was president. (some info from Wikipedia and The Wall Street Journal)