First if all, an accent is a way of pronouncing a language. Therefore, it's impossible to speak without an accent. Some people may think they don't have an accent, but everybody has one. The term 'accentless' is sometimes used- by nonlinguists- about people who speak one of the high prestige 'reference' accents (such as 'general american'), which are associated with people from a fairly high wide region and with people of high social class. Your accent results from how, where, and when you learned the language you're speaking and it gives impressions about you to others.
Languages develop different accents because, in all sorts of ways, we behave like those we mix with. When groups become distinct, the way they speak becomes distinct as well. This happens socially and geographically, but is easiest to illustrate by geographical differences. If one group splits in 2- say, 1/2 goes to Island A, and the other 1/2 goes to Island B- then once they've separated, their accents will change over time, but not in the same way, so that after just one generation, the accent of Island A will be different from Island B. If they stay separated for centuries, their dialects may become so different, it will sound like a different language.
Source: {http://linguistlist.org/ask-ling/accent.cfm}
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