Most everyone knows that the design of Renamon is based on that of a Kitsune, a mythical Japanese fox spirit (right). Indeed, in the original Japanese version of 3.25, "The Journey Begins," Rika's Grandmother believed that Renamon *was* a Kitsune. However, there's more to it than meets the eye, as several of Renamon's powers, actions and traits have their roots in the Kitsune mythology.
Kitsune are eaters of energy. They draw energy from other beings to feed themselves, draining the other being. This is mirrored by Renamon's absorbing data from her foes. A Kitsune can form a bond with a human, and they will be able to share their energies. A lot of the time, humans didn't want this connection. This is reflected by Rika's distancing herself from Renamon early in the series, but when she and Rika reconcile their differences and their bond strengthens, Renamon no longer needs to absorb data from other Digimon.
In 3.16, "Back to Nature, Back to Battle," Rika gives Renamon an energy drink, and Renamon happily remarks that it's her "first gift." While it may seem like nothing, gifts are an important part of the Kitsune legends. In order to stop Kitsune feeding on crop energy, people would offer gifts to them via shrines. The act of giving the gift fills a Kitsune's energy needs, so Rika's gift of an energy drink is both a nod to and pun on this.
Kitsune are said to be very earthly, sensual beings, although some would gain spirituality. If they followed the right rules, they would ascend to heaven. Renamon's following of the rules is reflected by her giving thanks for a meal in 3.44, "The Messenger." Kitsune spirituality is, in general, represented by all of Renamon's Digivolutionary forms, which are a mish-mash of Shintoism, Buddhism and Taoism.
Renamon's ability to fade away is an interpretation of a Kitsune's power to fold space, and create interdimensional pockets for them to travel through.
Thanks to Andromon X, Argemon, Ben-San Arizona, Steve Blum, Fenrir X, Neil Kaplan, Mary Elizabeth McGlynn, Christopher Miller, Minarvia, Jeff Nimoy, Hannah Parvin, Settou, SirSTACK, Dave Wittenberg, and especially AndyTaft/Andy00