“You are a foreigner, therefore you will always have a foreign accent”

This line is often used to discourage language learners from studying pronunciation seriously. You didn’t grow up in an English-speaking country, so why bother trying to get your English vowels right?

It is related to the Critical Period Hypothesis (see next myth).

Fact:
The fact that most foreigners have a foreign accent does not mean that you have to be like them. Many comedians are able to perfectly imitate the speech of actors, politicians, etc. Hugh Laurie was able to do a perfect American accent in House M.D., even though he is British. I can also humbly offer my own example — on listening to my speech samples, a number of Americans said that if they met me on the street, they couldn’t tell I wasn’t an American. (By the way, I have lived in Poland all my life and started studying English pronunciation at 15.)

There is no reason why you can’t speak a foreign language with a perfect, natural accent. You will need at least some talent for imitating sounds (if you can imitate people in your own language, that’s a very good sign). However, if you just don’t have the knack, you can largely make up for it with persistence and a little technology.

For example, you can record your voice with your computer and compare it with the proper pronunciation. This technique helps many learners see where their pronunciation is different from the original and lets them gradually make it more native-like.

You will also need to study phonetics. First, find a resource which has recordings of all the sounds of the language you’re learning (like the table with English sounds we have for English). Then, discover which sounds are used in which words by listening to the language and by reading phonetic transcriptions in dictionaries.

Perhaps you will not be indistinguishable from a native in the end, but you are likely to achieve clear, pleasant pronunciation that will give native speakers something to wonder about (for example, Michal Wojcik’s accent is confusing for some native speakers — they think he’s from an English-speaking country, but they can’t tell which one).

Further reading:
How to learn English pronunciation