I'm talking about a consumer level router. Does the router itself store any internet history from people connected to the router? Specifically I would like to know about the Apple wireless router but information about any wireless router would be helpful.
Not really in general. You could get access to dns/arp caching on the router, but that wouldn't tell you anything about individual users, and it wouldn't be a real accurate way to tell anything.
What people are doing beyond what addresses things need to be routed to is really none of the router's business in general.
Some routers do have logging options to get web page access, but it's not necessarily a standard feature. I'd look into individual models and check their logging capabilities.