Essential elements of game design

So, it seems to me that there are a bunch of competing qualities that make games interesting to potential players. Let's see if I can name and elaborate them here - kind of a Grand Unification Theory for game design. These are in no particular order:

1. Mechanics and Rules - A game design is essentially a request - come here, spend an hour doing this activity I've devised. The mechanics and rules define the activity, and therefore the request, and they'll determine in large part whether people will want to play the first time, and then whether they'll come back. This is clearly the most fundamental part of game design for most games, but not all - I'm sure many of you have played a game that has borrowed most or all of its rules or mechanics from another game, and relies on its art, its theme, or some other aspect to attract players.
2. Interaction - This can be positive (cooperative, party, or team games), neutral (games with individual decisions that affect others, like Monopoly or trading games) or negative (competitive or "mean" games, where you can block or hinder others' progress or steal their resources). There are some games that are fun with minimal interaction, but you start to shift from game to puzzle or hobby with too little interaction. Too much interaction, either positive or negative, can be bad too. The key is finding the right amount for the game's mechanics and audience.
3. Graphics and Components - This is probably more important than most people realize. You can have the best game design in the world, but if people are playing with ugly, crude parts, then they're not going to like it. Conversely, sometimes graphic design and part quality can carry a game that would otherwise not be worth playing.
4. Innovation - this is interesting, because it's terribly important for the initial gameplay experience, and for "buzz" at all levels - whether just between friends or in the broader media. If you can think up a new game mechanic, a new goal, or a fundamentally new kind of activity, you're going to get people to try your game, and maybe buy it. But it's not enough to make it the game you remember years later, or pull out every year at the holidays. More on innovation in a later post.
5. Fun - this is tough, because fun is definitely in the eye of the beholder, and no one game can be fun for everyone. Fun can be hard to capture or identify early in the design process, because often you focus on mechanics or rules before you worry about how fun your game is. Because of this, the pursuit of fun is often an iterative process in design - you design the game, then try it, figure out what the most frustrating or boring parts are, and try to modify the game to mitigate or remove them while amplifying and promoting the parts that are fun.

Let's leave it at those five for now. There are plenty of other important factors for game design, but you can lump most of them into these categories (especially into fun, which is the primary purpose of most games).