Should I paint door hinges?
Painting hinges is not a question of being better or worse. Depending on the motif, hinge finishes are often selected to complement the door or trim color.  For example: brass metal finish often used with tan trim/doors or natural wood finishes.  Chrome or brushed nickel hardware is popular with white trim/doors.  Hinges and passage sets come in a lot of different metal and colored finishes.

If you do decide to paint the hinges, resist the temptation to simply paint them in place. It is difficult to evenly paint all the surfaces of a hinge and not fill the slots of the screws. When painted in place, the paint will often chip if it dries and bridges the joints of the hinge. It tends to chip when you first open/close the door. I really try to avoid painting hinges, but when I paint new, previously unpainted hinges, I remove them, clean them well, spray paint them, screws included.