It can be heard in some cars when the player leaves the vehicle with the door open or if the door gets taken off its hinges. As it is very hard to hear, the best way to hear it is to go to a quiet area (such as the Old Mansion off Beaverhead Avenue) and to turn the volume up.
This is very realistic as most vehicles will not allow you to leave it open in real life as well.
The Door Ajar Chime is also present in Grand Theft Auto V. This time, most cars in the game have this feature, which is experienced when the player opens his car's door. The chime is fairly loud enough to hear on high to medium volume.