The 68-year-old former BBC star, one of the biggest names in British broadcasting during the 1970s and 1980s, denied a total of 15 charges.
Travis, who counts Myanmar opposition leader Aung San Suu Kyi among his fans, was appearing at Southwark Crown Court in London under his real name David Patrick Griffin.
He is accused of 14 counts of indecent assault between 1976 and 2003, and one count of sexual assault in 2008.
Wearing a green jacket over a white shirt, he replied "Not guilty" to each of the charges as they were read out by a court official.
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Travis spent 25 years presenting on BBC Radio 1, and also hosted a music request show on the BBC World Service.
He is one of several ageing celebrities in Britain arrested under Operation Yewtree, the police operation set up in the wake of revelations that late BBC star Jimmy Savile was a prolific sex offender.
The charges against Travis are not connected to his former colleague.
Travis is currently on bail on condition that he lives at his home and does not contact the alleged victims.