From what I can tell, the mark of a great game (and this could even be extended to many other venues of entertainment, like movies) is that throughout the whole, almost everyone* finds enough about it to like that it overshadows what faults they do find.
God of War acts as a perfect example in this case: I just got both games of the series, recently finished the first one and have started on the second. So far I'm enjoying God of War II much more than the first one, mainly because of the additional weapon choices (though I liked the magic of GoW better). What I like about GoW: The graphics, the story (simple enough to ignore if you wish, deep enough to look for more in symbolism throughout the game), epic scenery (running through a city and seeing a giant god in the background wreaking havoc...that sells the game to me on its own), and the hack-'n-slash combat. Brutal and elegant at the same time. What I don't like: quick-time events. or to put it more specifically, randomized-button QTEs. They make me feel like I'm playing a hell-spawned version of whack-a-mole. I have to focus so much attention on which specific button I have to press that I miss half the epic kill. Nevertheless I still love the game because I have the choice not to use it in the average fight, and in boss fights there is usually enough of a chance to regain the health lost in failed attempts that it doesn't make for endlessly-frustrating "you would have killed the boss, but since you hit X instead of O, he killed you instead" events. Well, not all the bosses are so unforgiving, luckily. I also don't like how easy it is to not use magic, but that's probably just a result of my play-style: Why use magic? Carving off the flanks of minotaurs doesn't use any mana! That I might need if a boss comes up soon! Instead of an inevitable blue-orb chest >.< oops.
Anyway, the point of all this is that some people love the QTEs, and fire lightning into enemies faster than previously-mentioned blue orbs can fly, but couldn't care less about the story or the glowy (awesomeness of) dual-wield swords chained to your wrists, but still find the game to be deeply enjoyable. It doesn't have to be universally and unanimously loved to be a great game, if enough of the angles one may view it from form a good shape that doesn't fall apart at the seams.
*not including people who just plain don't like whichever genre is in question. I can't stand sports video games, for instance. Or suspense-horror movies.