You do make some very good points, Tarasee, and practice is the key. I totally agree with that. However, I wouldn't want people to underestimate the importance of accents either.

You are right, native speakers are forgiving. But communication between native speakers and non-native speakers is just one side of the story. Communication between non native speakers is a whole new ball game. Non-native speakers, with time and effort, come to understand native speakers even when they themselves speak with a thick accent. But when it comes to understanding a non-native speaker for another country, it's murderously hard. 

To give you a real life example, I am from India. I work in an international company with teams from all over the world. I have absolutely no problem communicating with the teams from the US or the UK. But I have an incredibly hard time understanding Japanese or Chinese people speak. That's why I have come to prefer emails over talking on the phone. That's a complaint I have heard from everyone I know who had interacted with people from other non English speaking countries. 

So I believe paying attention to your accent will serve you well in the long run. 

Irene, 

If people judge you because of your accent then they are the one with the problem.  If they can understand what you are trying to communicate then the accent is simply part of who you are.  Now, if the accent is causing them to NOT understand what you are trying to say..then there is a need to work on pronunciation.

If you are noticing that you do not "sound" like everyone esle, and that is bothersome to you...then simply ask them to repeat the words you feel that you are mispronouncing.  Most people will be flattered that you are even trying.  

Never let "accent" stand in your way of speaking to someone else.  :-)

I joined an international conversation with different people of nations. It is hard for me to understand non-native speaking in most cases. I felt frustrated sometimes, yet, I can understand most native speaking which comforts me more. I am not very sure if it is a matter of accents or just merely intonation concerned.  

"with the accent, it is difficult to understand some of the things they are trying to say. It is the same for understanding native English speakers: if I talk too quickly, then my students do not understand me because of my accent!"----"Don't Fret the Accent"

   I agree that efforts to eliminate   "accents"  are  something of an extreme.

I agree that we all need to consider speaking more slowly   so that understanding is possible.

   The only time I have ever found an accent to be any kind of a difficulty  is when  it has the status of being what we call "thick".  Many people do not have "thick" accents. What they have are normal accents and their speech is quite understandable.

Mak,  

you make an excellent point.  I always encourage my students to remember they are talking to someone who is NOT a native speaker.  They must remember that even though they may feel fluent, they must match the speed with which they talk to the other person's listening ability.  Accent involves both: speaking and listening.  

Beginning with more trivial topics at a slower pace, will cause one to be able to determine the pronunciation rules that each person is following.  Once that is established, speaking at a rate of speed that is more understandable, is much better than trying to speed through a discussion.  

There must be an understanding that people from the UK use different vowel sounds and stress different syllables than Americans.  For example: A person from the UK would say FILET as FILL IT and stress the first syllable.  But an American would use the proper French pronunciation: Fee lay and stress the second syllable.  

So just learning English is not enough.  You must determine which English you would like to learn, British or American...they are different!