I don't know how many times I listened to the song "Galileo" by the Indigo Girls before I noticed something strange about it. I had the song on a mix tape (it was the 90s) that I often played as I went to sleep in my hut in Senegal.
One night I realized there was something very strange about the opening rhythmic line. I played it back, over and over, until I understood it. Ever since, I've thought this song has the most brilliant and subversive opening riff of any tune I know.
The opening rhythm is unremarkable until the guitar comes in (about 0:09 in the video). Suddenly, you realize that the opening rhythm started on a downbeat, not the beat as you had assumed. Suddenly, the entire riff rhythmically invert itself, with stressed beats becoming downbeats and vice versa. It's as if you inverted the stress syllables in a stream of gibberish and a meaningful sentence suddenly emerged.
What I love is that I can reproduce the effect over and over. The opening beat sounds like one rhythm, them the guitar comes in and it sounds like a different one, even though it's unchanged. No matter how many times I listen, it fools my ear every time.