Maybe because I can't sight-read well on piano, I end up memorizing piano pieces by the time I can actually play them. it comes very easily, even early on though.
It's a different story on saxophone, though; I can sight-read very well, but I have a really terrible time memorizing tunes on sax, even if I really like them. Maybe it's because I can look at my hands while playing piano? but even then, I don't have to stare at my hands to play a piano piece... huh...
But either way, if you ask me, serious performances should be memorized. Maybe this is my rock roots showing, but sheet music on stage is lame. Well, I forgive you orchestra guys, that would suck to memorize all that stuff.