God DAMN this is a tough one Lee. A friend of mine was lucky enough to have a Dreamcast (such an underrated system) and we would sit in class biting our nails all day until the bell would ring and we could all retreat to his house to sack out and play either Unreal Tournament or Shenmue. Very good balance when you think about it, once we grew tired of shooting each other to a bloody pulp, we took turns progressing through Shenmue. We couldn't believe just how detailed the game was. Years before GTA: San Andreas, Shenmue was already incorporating realistic elements like varying weather, interactive "stores" you could enter, mini-games, etc. The game was flat out amazing to play and really spoiled me on a lot of games forever. Every time a new game would come out being hailed for it's new innovative realistic elements, I'd sigh and say to myself "Well is it like Shenmue?".
Dune II is fantastic as well. I didn't start playing this game until a few years back, when I became interested in the Dune saga, but man am I glad I did. I mean, can you say "influential"? Without it, the real-time strategy genre would not be where it is today. I'm a huge fan of the RTS genre, so of course I adore Dune II. Add in the great story, and addictive gameplay, and it's a classic through and through.
In the end...I have to go with Shenmue, but man is it close. Shenmue though just took gaming to a whole other level and doesn't get the credit it deserves. I suggest anyone who has the chance, to play it immediately. This was definately the hardest vote for me to cast thus far though.