According to the New Mexico Space Museum, Virgil "Gus" Grissom was the first man to travel into space twice. Unfortunately, before his third journey into space, he was killed in the Apollo 1 fire on January 27, 1967.
Gus Grissom was the pilot of Liberty Bell 7 atop Mercury-Redstone 4 on July 21, 1961. He returned to space in Gemini 3 on March 23, 1965. He was the prime choice of NASA program directors to be the first man on the moon before his death in the Apollo 1 accident.
The first woman to travel to space twice was the cosmonaut Svetlana Savitskaya, who flew missions to the Salyut 7 space station in August 1982 and July 1984.