Could Time Travel ever happen?

Doctor Who hurtling through the centuries, hitting the controls inside the Tardis like some kind of metaphysical pinball machine? Or does it raise images of time-flying contraptions built by Victorians in velvet smoking jackets? Or time machines made from souped-up sports cars like in the Back to the Future movies? 

But could it ever really happen?

The probability of time travel is being investigated by academics at the University of Birmingham, one aspect of an international research programme into the nature of time involving universities in Australia, the United States, Germany, the Netherlands and Turkey.