Having an accent can be your greatest attribute. However, it can also be what thwarts you from obtaining work. It depends upon the extent of your accent, regionalisms in your speech, and where and to whom the recording will be played.
Typically, when a producer desires an accent, they desire a "neutral" one, meaning that there are no regionalisms. This way, when the voice over recording is to be played in the area in which the accent is indigenous - it will allow the listener to bond and 'feel at home' with the voice.
For most national work, a native voice without any regionalism is preferred - as the recording will not appear biased to any one region. This is called "standard American English." For example, a recording being played across America would use standard American English, and would typically not have a New York or 'Southern drawl' regionalism, etc.
For international work, the same thing goes: Use a voice that is "neutral" to that country (one that does not have regionalisms within that country).