Apple has always publicly distanced its products from the video games market, preferring to offer a platform where developers can thrive on their own rather than competing head-on with established giants. The runaway success of the company's various iThings put it right at the center of one of the fast-growing sectors of the gaming industry today, however. I think the launch of Game Center last year is a direct result of that, as are some newly discovered patents which suggest that avatars are coming as well.
Two separate patents filed by Apple in April point to an interface that will allows users to create customer avatars in Game Center (via AppleInsider). The demo images included with the patents show distinctly Mii-looking avatars, though that's not necessarily indicative of what a final version of the feature might look like. The patents allow for these avatars to be linked with and used in Game Center profiles and titles, much like what you see with the Xbox 360 and Wii.