According to Dr. Joy Hirsch a professor of neuroscience at New York's Memorial Sloan-Kettering Cancer Centre and senior author of a study published in the current issue of the journal Nature, "A second language acquired during the teenage years, which is later in developmental life, is represented in the brain in a separate location from the native language. But when bothy languages are learned at the same time early in life, they are represented in areas that have a considerable amount of overlap".
If this is the case, we have to think that all areas of the new language such as pronunciation and accent are stored in a separate "drawer" of the brain, so in my opinion, an adult whose second or third language is stored separately from his native language will always speak with an accent.
Now, he can practice his pronunciation and improve it, and he can be very successful in getting people to understand better what he says, but he will never sound as a native speaker.
I have seen in little kids whose parents speak to them in one language and they learn another one in school that they speak the first with an accent, even at that early age!
I think each one should be proud of their own heritage and not worry about speaking (English, because that is the most ocmmon case) with an accent. Living in such a multicultural city/country, I, personally, enjoy meeting people with different backgrounds and listening to different pronunciations, it enriches the language and its actual culture.