Although the norm is to paint the doors the same as the trim don't feel pressured to do this. Technically, the doors are another functional component and they can be accented. If you like the doors black leave them black and paint the door frames as well as the other trim pieces another color.
Example- The trim (door frames, base and casings) throughout your home can be white or off-white while the doors remain the current black color. This does look good in my opinion and really sets off the doors from other design elements.