For me a perfect game must have a great story with it. Doesn't have to have a ton of dialog but must have a great story that will suck you into it. I like to feel like I am the main charictor going through the story, and lose myself in it. Like Wolf pointed out Chrono Trigger, they did a great job in that. Silent protagonist never made you feel like you were saying something that drew you out of the story. Fable also did this well early as your choices would either make you good, or evil and the world around you shifted into what you chose.

Music is also very important. Like Peter mentioned. Where he said it was the heart and soul of the game, it is true. It can change the mood you feel at anytime helping you understand and feel what the developers are wishing you to feel at that moment. It is a simple yet proven way to keep you engaged in the story, while aiding you in the way you should feel at the time. RPG's do this well using Chrono Trigger yet again as an example, when going through the future the music is dreary like there is no hope. Once Crono, Lucca, and Merle decide they must do something the music changes yet again to a victory upbeat music that pulls you in the direction of we can do this! Though before you head back to the present the dreary music will play again showing you you are not there yet and you must work for it.