There is wide variation from person to person in terms of how they heal after minor and major wounds to the skin. A lot of this has to do with genetic variation in terms of how the skin heals, and this does not necessarily mean that you have a particular condition that you should be tested for.
When the skin is damaged, new cells migrate into the damaged area to close the wound and produce the new skin. Part of this response includes inflammation in the wound and the migration of cells containing pigmentation as well as an increase in the amount of small blood vessels in the are. Therefore, pigmentation of the healed scar is a normal part of the healing, and this post inflammatory hyperpigmentation, as it is called can take weeks to months to fade away. If you skin is very fair, as you say, then this pigmentation can be even more pronounced.
Unfortunately, there is no real treatment for this process, as it is a normal process. What you can do is make sure to protect your skin from other forms of damage, such as sun damage. Also you can apply an antibacterial or other occlusive ointment to cuts and scrapes to promote healing.
Talk to your primary care doctor
if you have more questions.