Actually, it's a misconception that great games are based around "fun." In reality, games that are truly successful are based on motivation. People don't play games for an extended amount of time soley because they are fun. They'll find a "fun little game," play for one or two sessions, then forget about it. I can't even count (or remember) a ton of the fun Flash games I've found online. They were lacking any motivation for me to come back night after night, though, and play. This is just one example.
Mario, as you mentioned, had an exterior motivation that was very much beyond just fun. People were amazed at what could be done with games, and wanted to see the story unfold (a very population motivation technique) and explore new areas of the game.
Some games have a different style of motivation. Tetris, for example. This game is based on the fact that you play it mostly when there isn't much going on. The motivation is to occupy your mind with something other than the "real world." This is a common theme with portable games, especially. Another example along these lines: the rubik's cube. This isn't really fun, but it's motivating to complete. When it's finished, we rejoice in our victory, and this is fun. We find it challenging (which is not the same as fun, although the two can go hand-in-hand) and this challenge motivates us to accomplish something that is presented as being intended for us not to complete. It's the human nature of "this can't be done? Let me try..." It's a huge motivator to get people to buy into the hook of your game.
You guys are mentioning good graphics. YET more motivation. You wonder what cool cutscene is coming up next...how these awesome graphic, character, and animation design will give you more of the immersive world surrounding the game. What's going to happen next?
Yet another example: World of Warcraft. You can't argue the success of this game by any means, and...let's face it...a lot of the game isn't all that fun. It isn't fun to shoot your 3,000th shadowbolt at the 428th level 2 zombie that you're killing for the night. But there's motivation in it. Level up, see the "cool" stuff in the game, and experience fun at THAT point with your friends. Motivation STILL persists here, though, to either get better and better gear, or to pvp with other players for various rewards. Overall, though, a good chunk of the game isn't directly fun.
A lot of games that involve player development through character growth center around allowing a player to become immersed in this experience of advancement. They believe that THEY are becoming something more than they are...that they're exceeding boundries put on them by reality. This is where good animation and great world/character design *can* come into play, although it is also often accomplished through other methods. Although you may call this fun (and often times portions of it are, of course), there are always stretches in games that aren't fun. You can't avoid this, no matter how good you may think you are at design, because everyone has different thresholds of how long they can stay at something...how much of your challenges they can take. This is where truly successful design gives motivation to either keep playing or come back later. When the player is away, you instill a sense in them that they're missing something...your game.
So, in short, fun is important, but just "fun" doesn't make great games by any means. You can make some neat little Flash passtimes by making games soley around fun, but if you want to create a truly great game that people will want to come back to again and again, you need to find that motivation that makes them never forget the title you put on your box.