Is your original language something other than English? While English is claimed to be the international language of business, it is not the most common natively spoken language. Mandarin is natively spoken by 14.1% of the world, Spanish is 5.85% and English is 5.52%. As far as languages spoken, Mandarin is still #1, English #2 and Spanish #3.
In Toastmasters, we are often approached by people who worry about the clarity of their English accent when public speaking. First, almost EVERYONE has an accent of some kind. Second, if people like you, they will want to understand and be understood by you. After a few moments, we condition our minds to process your words and soon we barely notice it - it's just part of the magical you.
(2013 Update) Here are highlights of Presiyan Vasilev, from Bulgaria, winning the 2013 World Championship of Public Speaking.
Here is a contest-winning humorous speech by native Russian, Vitaly Terekhov, "Are you Married or Happy?"
In the same way, just start speaking. Hold on to your accent. Like Harvinder and Presiyan, it is part of your charm. Let's celebrate all languages and cultures.
If English is your second language (ESL), or third, or fourth, and you are interested in building a more North American English accent, for use sometimes, here is a series of videos by voice talent, actress, and director, Amy Walker, to help you.
Click here for the whole 4-part video series on developing an American, or North American accent.