I've been accused of cheating once in my life, and even I was almost convinced. Allow me to set the scenario.
I'm playing hold'em at a ten person table at a local bar. I was traveling with a friend of mine who was dealt pocket aces twice in a row. That happens sometimes, but it raised suspicion in one conspiracy theorist at the table. She noted that I was dealing one of those hands and my friend dealt the second. No one else at the table seemed to care.
The immediately following hand I was dealt pocket aces. The hand after that I was surprised to see the aces again. That was four times in a row AA were the hole cards for myself and my buddy combined, and every-time the aces won the hand in a showdown. We weren't cheating, but we were beating the odds incredibly. It was awkward handling the table from that point on, and the girl who complained about the first two came out and accused us after the second two hands. Before she actively lobbied for us to be kicked out of the venue, someone else at the table pointed out she herself dealt the last hand in question.
In a way I felt flatted that she thought I was such skilled a mechanic. The lesson I learned here is that although you should always be aware of suspicious behavior, a streak of luck alone may be just a streak of luck.