I had no idea it was p2p. I have been of course marveling at how instant everything is, from playing a new song to skipping ahead inside of a song, but never really put much thought into it.
It's actually a hybrid. The most frequently played songs are on Spotify's caching servers, and the first ~15s of those songs are streamed from them. The rest of the song is streamed via P2P, as are the entirety of the less frequently played ones. I seem to recall also that Spotify will locally cache songs you play frequently as well.