Magic can be inherited any number of ways in fantasy worlds.
Those with magically skilled ancestors usually inherit powers-occasionally more power than the ancestors. This power manifests itself in early childhood, but doesnt reach maturity until the child does-usually on the eighteenth birthday. I've also encountered stories where the child's innate magical ability is not unlocked until a certain event, or sequence of events has come to pass (finding a certain sword, making a journey, etc.).
That does not always exclude others from using magic. Magic can be learned. The amount of magic one can learn is usually determined by their intelligence-usually scholarly sorts have the best luck. Wild men usually gain their powers by being as close to nature as possible-therefore gaining the ability to channel natures power.
Magic can also be gained through the use and weilding of magical artifacts. This can be an amulet, a sword, etc. These powers may be permanent or may wear off when contact with the artifact is relinquished.
And finally, magic can be bestowed upon a person. Either by another magic weilder, or some sort of powerful spirit (godly or otherwise), the ability to use magic can oft be granted. This is usually the case when a certain quest needs to be performed, and either the person "fated" to finish the quest dies or disappears mysteriously, or turns evil, etc. It may also be the case when a tournament of sorts takes place, to decide on who will go on the quest. The winner of the tournament usually receives some diving ability.
I think that the above modes of magic inheritance can be inherited to just about any fantasy work. Comments?