By the accepted definition of the word, our dog Bailey is not well trained.
If we sent her out to fetch the paper, it's highly unlikely she'd ever return. She jumps on strangers and mauls her friends. Every morning she steals the bath mat; every night she gnaws her leash (and, when that fails, she tries to pull my shoulder from its socket).
But we love her anyway. We're dog people, and she's a people dog. I'd do anything for Bailey, including wrestle an overly aggressive Bernese Mountain dog (long, embarrassing story). According to Jon Katz of Slate, maybe she's better trained than I thought.
Consider the possibility that pets are, in evolutionary terms, manipulating human responses, that they are the equivalent of social parasites. Social parasites inject themselves into the social systems of other species and thrive there. Dogs are masters at that. They show a range of emotions—love, anxiety, curiosity—and thus trick us into thinking they possess the full range of human feelings.
While the whole not-peeing-inside trick is still my favorite, I have to say her ability to slyly manipulate my emotions for food and shelter is quite impressive.