This is a very common question I hear from immigrants and overseas workers as we discuss their coaching options.  Though everyone’s case is unique, here is my general advice:

If your (heavy) accent is stopping you from being confident, from making friends and/or from making (more) money, then YES.  Do some accent reduction for your own peace of mind and to become a more confident speaker.

If your accent does not interfere with daily communications, and people are not constantly asking you to repeat yourself or say it again in a different way, then you are probably okay.  You still may choose to modify your accent anyway, but at least you should know that it is not a pressing issue that will halt your career.

How can you modify and reduce your accent?
1.  Watch English movies and TV.  Rent DVDs of shows and sit-coms and play them over and over again, with and without English subtitles.
2.  Listen to the radio and/or sing English songs.  Look up the lyrics online.
3.  Meet native English speakers and practice.
4.  Buy a good pronunciation book, preferably with audio CDs, MP3s, podcast etc.  Choose carefully BrE or AmE.
5.  Attend Toast Masters or another public speaking practice forum.
6.  Attend an ESL class that focuses on pronunciation or lots of speaking practice.
7.  Hire an ESL tutor who has experience teaching the above, or whose voice you want to imitate.  Don’t be shy to ask for details of experience, materials used, references etc.
8.  Hire a professional Communication Coach with a solid background in ESL and accent reduction.
9.  Hire a professional linguist or speech pathologist.
10.  Practice practice practice.