Most of the people in my country, India, speak English as a second language. As you may know or may not know, India had been under British rule for a long time. However, the variety of English we speak is not intelligible to most native speakers. So, the accent does make a difference, doesn't it? Had the Indians spoke in British or American accent, the natives would have been able to understand them clearly.

@Noyi I lived in an area in the US where there was a large community of people from the entire Indian subcontinent, and while, yes, there was a noticeable accent when they spoke English, I never had an trouble in understanding/communicating. I can see, however, if someone doesn't have a strong command of English and they meet a person with a very strong accent that deviates from the standard we know from the mainstream (movies, news, etc), they might have a problem speaking with each other. But I can only go from my own experiences and from those around me.

@HannaYou
Because the Indian people who live in your area have been living there for long, they're constantly exposed to the accent of that area. It being so, they have an edge over the English speaking people living in India without exposure to American English.

I fully subscribe to your views. I do like your musical instruments analogy. But, put it simply, my question is whether it is possible to speak without an accent.

I mean from the point of view of a native speaker

@Noyi Then I would have to reword your question to: "How easy is it for anyone to mimic the accent of a particular group?" The answer is: "It depends!" Any human child at birth has the ability to reproduce any sound in any language. With age, we all specialise in a fairly narrow range of sounds, a grove that becomes increasingly set after puberty. With a good ear and practice, most of us can learn to produce most of the sounds in any languge even later in life. However, some sounds are harder than others for some. The English "W" and "R" are mysteries to most non-Anglophone Europeans. I teach French to Anglos and very few of them master the vowel sound in "feu". I think the big issue is training the ear to listen to different sounds rather that the actual production of sounds. Some differences are quite subtle. Arabic, for instance, is language of consonants. Vowels, such as they are, are normally not even written. So an Arabic speaker would find it difficult to distinguish among, English words such as "hill, hall, hull, hell". They would all sound the same whereas an Arabic sound such as "ain" absolutely does not exist in English.. Hmmm. I have run on a bit. To answer your question directly, it is not possible to speak without an accent. It is possible to speak with a different accent, but one must listen really hard! Most people cannot be bothered.

@amymcmxcii
You're absolutely right when you said "With a good ear and practice, most of us can learn to produce most of the sounds in any languge even later in life." But the fact is that, at least from my experience, however hard you try to listen, you won't "hear" certain sounds in a foreign language. When an American speak, normally I can make out what he or she says, and I know the points of articulations of almost every sound, but when I speak the same sentences observing all the rules of phonetics and phonology, I drastically fail to sound like the American.
I can't understand the inexplicable reason behind this phenomenon. Do you have any idea?

Btw, you say there are only consonants in Arabic. But the sound represented by "alif" is a vowel. Also, by using diacritical marks above or below a consonant letter, you can make a consonant+vowel sound. For example, put a kasar below the letter b and it becomes bi (consonant+vowel)

Anyways, thank you for sharing your knowledge with me. And I'd like to hear more from you.

@Noyi Last things first! I didn't say Arabic had no vowels; I said it is a language of consonants, meaning, consonants are significantly more important than vowels. I wasn't clear. Alif is not a vowel but a glottal stop, close to the "T" sound in "bottle" or "butter" as pronounced in certain British dialects. The syllabic short vowel diacritics are normally omitted because usually the meaning is clear from the consonants.

It is no mystery as to why you, or I find difficulty in perfecting an accent or language. Knowing how to do it is not enough. One needs training, time, and practice. It's like sport. One can know all the rules and techniques required for football and still have no chance of reaching a professional level. Techniques must be totally integrated not just understood at an intellectual level.

@amymcmxcii
I have to admire the depth of knowledge that you have in the realmof languages.