If you listen to the first 40 seconds or so of Veridis Quo by Daft Punk, you'll probably feel like you have a pretty good idea of the beat of the song, each of the chords starting on the first beat of each bar. Then at about 40 seconds the drums fade in and you (or at least I) discover that you were wrong; what you thought were downbeats were really upbeats and vice versa.
There's a similar but maybe even more pronounced effect in Pyramid Song by Radiohead, where it's hard to even pin down what's going on beat-wise until about 2:15 when the drums come in and you realize that what you thought were five repeating quarter notes separated by a weird rest are really dotted quarter notes.
Is there a word for this kind of weird sort of beat ambiguity that is resolved when a rhythm instrument comes in? Can you come up with any other examples of this?