Gaius has some positive associations that others here have already mentioned, but it has one negative association in that it's the actual first name of the cruel Roman emperor who couldn't escape the disparaging boyhood nickname of Caligula (Caligula could be translated into something akin to "booty-kins." Gaius was called Caligula because of the shoes his mother made him wear as a child).
Gaius was the first name given to Dr. Baltar in the reimagined "Battlestar Galactica" science fiction TV series. Played by British actor James Callis, the character is notable for inadvertently giving the Cylons the means to commit genocide against the twelve colonies. The character also is highly intelligent, amoral, and highly self-centered.
Gaius Caesar (Born Gaius Vipsanius Agrippa) was the eldest son of Julia the Elder, daughter of Augustus and her husband Marcus Vipsanius Agrippa, a famous Roman general during the late 1st century BC. He and his younger brother Lucius were adopted by their grandfather Caesar Augustus (their mother’s father) and Gaius became the heir to the throne, however both he and his brother died prematurely in AD 2 and 4.
Augustus' birth name was Gaius Octavius Minor. His father was Gaius Octavius Major. His eldest grandson, son of his only daughter Julia, was Gaius Vipsanius Agrippa (Later Gaius Caesar).