I take my being emotional with a game to be a good measure of the game's quality. While very few games have immersed me to the level of Tsukihime (had me in tears at various times for, oddly, various reasons), Fate/Stay Night, or Tales of Symphonia, I still get into most of the games I play.
Whether tears of horror during Tales of the Abyss (Akzeriuth), my throat constricting slightly at the end of Devil May Cry 3 (followed by elation), pure shock at the two major twists in both Baten Kaitos games...
It's one of the reasons I absolutely want to play Kana: Little Sister, but I know I absolutely must not, because it would destroy me.