Here follows a chart that I believe covers the shades of accent one can have while speaking a foreign language (i.e., a language consciously learned as an adolescent or an adult):
0 – unintelligibly thick accent – prevents communication as they just cannot understand you despite your relatively correct structural expression
1 – problematically thick accent – leads to miscommunication and misunderstanding as they tend to think you are saying something other than what you are saying
2 – offensively thick accent – they understand you, but you grate on their ears
3 – stereotypical accent of distinct origin – whenever you speak, you are immediately identifiable as being an American or whatever else it is that you are
4 – alien accent – they may not know just where you are from, and they may not draw attention to the fact, but whenever you engage new conversation partners, they do register the fact that you sound somehow unnatural or foreign or idiosyncratic or weird or strange or funny, etc. depending on their individual sensibilities
5 – accent moot to communication – they listen to the meaning of your words first and foremost, but if given reason or pause to reflect, they will recall that you sound distinctive or somehow different and thus that you are probably not one of them
6 – polished accent – they can tell you speak their tongue because it is a learned language you have studied rather than grown up with, and that you have worked carefully and hard at doing so (“like a diplomat,” i.e., comparatively much better than most foreigners manage)
7 – accent of (seemingly) long residence – underlying traces of your native tongue remain, but your intonation and overall delivery sound very natural
8 – near native accent – you may be taken for a native at first, but a phonetic irregularity or two eventually betray you
9 – native-other accent – you are taken for a native speaker from another region of the language
10 – native accent – people from a given region believe that you are one of them
Obviously, 0, 1, and 2 are undesirable, though many learners struggle long and perhaps in vain to transcend them (your average East Asian speaking a Western language, and vice versa). Although it is the best they can do, 3 also generally carries a stigma in the minds of many speakers. Even 4 might seem less than ideal, though it is the top level managed by many linguistically talented and highly intelligent individuals who have otherwise attained complete fluency and accuracy of expression (e.g., the English of Michel Thomas). 5 is probably ideal (the best compliment is no compliment—if they tell you, “you speak really well,” what they are generally truly saying is, “I notice that you are struggling to speak well, and I know how hard that is—keep it up, you’re doing a good job!”), though 6 is nicer and more respectful, especially if you really care for a language. This 4-5-6 range is indeed both what I generally aspire to and what I would recommend as a realistically attainable goal. 7+ generally require many years of residence in the language, though those with special talent and/or who make special effort may attain this range otherwise. I do not believe that 10 is inherently impossible, but I personally have never met anyone who has attained it.
No other aspect of language acquisition is more purely dependent upon raw native ability or talent than is accent. By working hard and intelligently at improving your structural knowledge or vocabulary, you can logically expect to continuously and measurably increase your reading ability and even your range of correct active expression, while comparable time and effort put into accent amelioration is likely to produce far less noticeable results. You should obviously strive to do your best, indeed, to aim high in the hopes of hitting near the target, but you should keep your perspective and recall that most people reach a permanent plateau at 3 or 4, while those who do get to 7 do so by putting in the time. Thus, you should avoid becoming obsessed with sounding like a native as this can cause you both to spend excessive time and energy on this to the determinant of your own holistic development and to be uncharitably judgmental of others; furthermore, it is actually a dangerous goal to obtain, as sounding like a native, or even just sounding as if you have a better overall command of the language than you really do, can easily get you into trouble.
