Zone of the Enders is by far one of my favorite games/series to date. It has a solid storyline, likable characters from the beginning of the first game, through to the end of the second game, and even in the GBA tactics game. The music is absolutely astounding, when playing through both of the ps2 games, the music helped set the tone so many times, I knew a big fight was about to take place or when things were emotional.
The second one was the first time I can remember seeing Cel-Shading on a ps2, and I lost my mind, it's still one of the most beautiful games I've played (and I'm extremely biased) and I do plan on picking up the HD remakes for Ps3 when it comes out. I just wouldn't feel right playing it on a 360 =/.
Though, since Z.O.E isn't on there, I'll go for another Kojima favorite of mine; Metal Gear =3.
The Legend of Zelda Assassin's Creed : Too young to be called a franchise imo. Sonic : When you see the descent to hell that this poor hedgehog undergo... Though some late Sonic games were actually good it seems. Halo : Not my type. Final Fantasy : I don't trust Square-Enix like I trusted Squaresoft. No longer my favorite franchise since a while. Resident Evil : Not my type. Metal Gear : Hmmm... Good one, but not my favorite. Mass Effect : Nay. Mario : Well, let's be honest, the italian plumber was figured in many good games. Not my favorite franchise, but one which I respect. Other : I don't really have a favorite franchise. I would have say the "Mana" franchise, but after Seiken Densetsu 3, things went downhill from there.