To me, one of the most important things in designing a game is designing the space of the game. The "map" on which things take place.
It's not always a map, obviously. A game like Civilization takes place (mostly) on an actual map... as does a first person shooter or a match-three puzzle game. But plenty of games don't use a landscape that is recognizably a map, or augment their map with other not-so-mappish landscapes.
As an example of augmentation, an RPG may use a "real" map for the walking-around bits, but will use abstracted landscapes for battles and skill advances. These spaces are still "maps", although they are usually much-simplified "graph"-style maps like you find in board games.
Sometimes, a game has no "map-like" terrain at all. For example, most card games do not have you laying out a meaningful terrain. But they still have a method for what cards can interact with what cards - those rules and the slots your cards can fill are a very simple space. They are much simpler than, say, a continent in Civilization, but they are still a space that most of your play happens on.
Generally, the game takes place on this space. The connectivity of the space - the "bumps" and "valleys" and "obstacles" and native "stuff" - affects how you play. If your city is landlocked, you don't get ships. If your RPG character encounters a lava stream, he'll have to find some way to get across. This "bumpiness" in the space of the game is what gives the game much of its flavor.
I'm avoiding the term "rules", because I think the term is a little inadequate. It's both too large and too small for what I'm talking about. I'm also not talking about "gamespace" as in "all the potential ways to play through the game". I'm talking about the space in the game: the terrain, if you want.
For example, the "rule" that a specific sword does extra damage doesn't have anything to do with space... although it may change how you can travel through the space. On the other hand, if one room is filled with underdressed ladies, that's not a "rule", but it will change the nature of the space and make it more or less attractive to various kinds of players. As I've said before, a game is the sum of all its parts, not simply the rules.
BUT... this view is a little simplistic, isn't it? A game is definitely more than a space!
Well, in some cases the game is almost entirely the space. Frogger, for example. Or Pong.
But in a lot of cases, the space of the game is affected by the player's actions. The space of a chess board is uniform, but the position of the pieces gives it a powerful texture. In essence, while playing chess the players build a game space with all its bumps and nooks and grooves.
Similarly, in Civilization, the world map is a space... but the game is not about just exploring that space! The game is about taming and inhabiting that space, and there is another space "on top" of it that is all about researching better ways to tame and inhabit...
Even in an FPS, where most of the space is pretty well set in stone, the way a player interacts with the space changes dramatically as the player gets various weapons and/or vehicles. A window overlooking a courtyard is not even worth noticing if all you have is a shotgun, but as soon as you get a sniper rifle, it's THE place to be.
My last post was about how letting players put bits in space is a good way to get player-generated content. This post, obviously, is on the same basic theory.
I've run a lot of non-computer games, games of all sorts. I've run Nobilis, the ultimate tabletop RPG. I've run Kung-Fu the Role Playing Game the Collectible Card Game 2: the Electric Boogaloo, a game which almost certainly caused a ten-point drop in some student's grades: I unwisely ran it during finals' week. I've run everything inbetween.
What I've found, universally, is that there are two things that players love doing: exploring space and building space. And what they seem to love best is doing both.
Now, of course, there's a lot of different kinds of space. Some players are in it for the social experience. They don't care what level they are, or how much damage their fireball does. Instead, they love seeing what others are feeling, or what relationships they have... and maybe they love building a world full of people feeling emotions and having relationships.
Of course, even that's oversimplified. Apples to Applies is a very social game in which you can explore and build a social space in the real world, very easily, very quickly. A lot of people hate it, even if they're the sort of people who love putting on grease paint and playing Vampire: The Masquerade LARPs. Maybe they need the fantasy setting (it does provide very different social dynamics). Maybe there's some other element they like. It's hard to say, although it's an interesting avenue for investigation.
In my games, I've come to automatically build a certain way: I put out a space for the players, and then I put out rules that allow them to interact with and alter that space. I often put out layered space, too - a social space over here, an adventure-world space there, some weird metaphysicky space underneath...
Any way I do it, the key is this "adjustable space". It's not a world where I dictate all change. It's not a world solely for exploration, but nor is it a world solely for building stuff. The fact that it allows for both (and either) lets me draw in a variety of players with a variety of interests. (Pacing is a serious issue at that point - probably the biggest issue - but it's not a terrible issue to have!)
To create the right type of space was originally a challenge, but I've gotten so used to it that now I find I don't even have to think about it much. Here are some observations I've found to work, although I don't really have a formula as such.
1) Space is a connective force.
Any space you build is for the purpose of connecting things to other things, and moderating those connections. If you build an actual map, things like mountains, rivers, and roads change the way that people travel across the map and therefore change what is appealing, defensible, etc.
For less literal spaces, such as the "space" of a card game, the connections can be much more explicit. "Creatures can attack creatures, but not enchantments or spells", "turn phases are always done in this order:"...
In a social space, the idea is to give certain players reasons to get to know each other, and others reasons to avoid cooperating. This creates "walls and roads", allowing you to make the social terrain interesting. It takes some practice (and, occasionally, math and graphing) to make this social terrain worthwhile: I'll talk about it some other day.
2) Space is seeded.
While you can just give out empty space and let your players get to work, this creates a very high entry barrier and extremely high early "difficulty" level, as they have nothing to work with. (I've made this mistake a few times... um... in the name of research! Yyyeah...)
It is important to put stuff in your space to make exploring/inhabiting various regions more or less important/appealing. In some spaces, this is a fundamental part of the space or the gameplay.
For example, in a CCG, the space starts empty, but you have very few options as to how you're going to develop it. In a social "space" such as the social part of a LARP, the people themselves are the space, so it comes pre-seeded with both character sheets and the personal presence of the player.
But in a lot of cases, the space needs to be pretty densely populated, and by more than simply roads and walls. Rivers and mountains and plains are all well and good, but a gem mine or a herd of elk will really make some place stick out as particularly nice. Similarly, an RPG world comes pre-inhabited by cultures and plot-tastic elements, even if you are going to rely on the players to do most of the heavy lifting. (Which is not very common in mainstream RPGs, but far easier in high-power RPGs such as Amber, Nobilis, etc.)
3) Space is adapted.
The last "great rule" of space design, at least for me, is that space is adjustable. Players can change both the first and second elements with enough effort.
Players can erect new walls or tear them down and build roads. Players can seed new resources, or transform areas.
In social landscapes, this is already pre-started for you. If two players really want to get along, nothing you can do will stop them, no matter how stridently your character sheets point out that they're enemies. The opposite is also true.
But that's just a start. The players need to be able to change the terrain's values as well as knocking down walls or building roads. This would mean, in a social situation, creating, destroying, or morphing the social resources people have. Their attractiveness, their in-game power, how much they know, how much they seem to know, who they have sway over, and their character's personality.
In other systems, such as a real map, the players must be given the same abilities you had in building the space originally. Obviously, balanced versions.
Even in CCGs, the players need to be able to create loopholes or weirdities in the simple space of the game. Thus you get the special abilities. "Trample", "cannot be targeted by green creatures or effects", "swampwalking", etc, etc, etc. These create an interesting, complex space built by the players. It works the same way as any other space.
I'm not saying that all games need to do this or this is the holy grail or yadda yadda yadda. I'm just saying that this is how I design my games, and it seems to work.
It's a lot easier in non-computer games, though...
I'm also saying that I think I've had too much caffeine at the moment.