TL;DR - 9 people have been called Captain America to-date
This information has been summarized from the excellent article on comicvine.
Steve Rogers - the original and the person who spends the most time as Captain America. Steve has primarily used two versions of the uniform.
Isaiah Bradley - another test subject for the super-soldier serum. He acts as a super-soldier after Steve was lost. He steals Steve's extra suit and shield and uses it on one mission and is then arrested and court martialed for doing so. It should be noted that he was never officially titled as Captain America, but was considered to be "the Black Captain America" by reputation.
The Spirit of '76 (William Nasland) - becomes the first published replacement as Captain America. He is killed by Adam II in 1946. Nasland wears the classic uniform.
The Patriot (Jeff Mace) - becomes the next Captain America. After his Bucky is replaced by Golden Girl, he eventually quits and marries Golden Girl. Mace wears the classic uniform.
In 1953 William Burnside finds the super-soldier serum and undergoes plastic surgery to look like Steve Rogers, but the project is cancelled and he becomes a teacher. He later meets Jack Monroe and the two use the serum to become Captain America and Bucky respectively. However, due to not using the Vita-Ray process in conjunction with the serum, they go insane. The government shuts them down and places them in suspended animation. Burnside wears the classic uniform.
Namor finds the Inuits worshiping a figure in a block of ice and throws the block into the ocean, where the Avengers find and rescue Steve Rogers. Steve returns as Captain America. Rick Jones becomes the new Bucky. Steve wears the classic uniform.
After the Watergate scandal, Steve Rogers becomes Nomad and Roscoe Simons becomes Captain America. Simons is eventually killed by the Red Skull and Steve returns. Simons wears the classic uniform.
Steve begins resigning as Captain America when the US Government starts forcing him to work solely for them. John Walker becomes the stand-in Captain America when Steve refuses. Walker eventually becomes US Agent and Steve returns as Captain America full-time. Walker wears the classic uniform.
During the Sentinel of Liberty storyline, Steve is briefly presumed dead during issues 8 and 9, The Falcon (Sam Wilson) takes over as Captain America for one issue (#9). Sam wears the classic uniform.
After Steve is apparently assassinated following the Civil War, Tony Stark follows Steve's instructions in a letter and finds and saves Bucky Barnes. Bucky becomes Captain America and remains as such even after Steve returns to the present time. Bucky is the first new Captain to wear a significantly redesigned uniform.
After Bucky is apparently killed, Steve Rogers becomes Captain America again.
When the Super Soldier serum in Steve Rogers is neutralized, Steve rapidly begins aging. He appoints Sam Wilson as the new Captain America. Instead of just wearing Steve's old uniform again, he wears an updated version of the classic design with Falcon's wings integrated.