I love mysteries, where you're not told exactly what's going on and have to find out for yourself. Myst and BioShock were great, and I loved LoZ: Majora's Mask because the backstory unfolded as we went, we weren't presented with our objective and the reasons behind it right away.
I also like games that take an established, formulaic franchise and shake it up, doing something new. Again, Majora's Mask was good because of this, and FFX-2 is one of my guilty pleasures. Super Mario RPG: Legend of the Seven Stars is also fantastic.