There are several different theories on board game design. I've watched the evolution of board game design over the past decade--heck, I'm still revising prototypes I slapped together ten years ago--and came to the reasonably obvious conclusion that there is no one hard and fast rule. Like so many other forms of art, design, and recreation, the definition of a board game is broad enough that it doesn't lend itself to compartmentalized desginations.
However, that doesn't mean we can't look at the different approaches to go about designing the rules and theme of a game. This is, of course, a broad look at things, and there are no doubt many that I'm forgetting.
All Rules, All The Time For years, this was the default way of doing things: if you invented a new game, you had to add new rules to an existing concept. The existing concept was successful, so the easiest and presumably best way was to find some way to tweak it. What you saw was an endless parade of overly complicated games that had a similar feel to previous games but with the added frustration of "innovative" rules that were usually just chrome and confusion. Of course, that's not to say that the large rulesets are necessarily bad--good games can come out of those. However, the vast majority of these games are wargames, and they kind of have their own set of rules to play by anyway--and the others are usually those that have a weak or nonexistent theme and need some "flavor" in the form of unnecessary restrictions. The best way to make this work is to make the rules flow with the game, as opposed to stopping the game.
Everyone Is Equal! Many players and designers strive for elegance--and for many, this means making sure everyone starts off the same and has the same opportunities as much as possible throughout the duration of the game. All of the rules apply to all of the players equally all of the time, and so no player can blame bad luck or poor starting position or suboptimal choices by another player. The winner is the one who truly played the same game as everyone else and still came out ahead. Once the purview of abstract games, most eurogames now fall under this category, and nearly all games tend to address equality amongst opportunity. Personally, I find this approach to be booooring, but I understand the sentiment.
The Players Are The Rules For those who like the idea of equality but dislike the symmetry that comes with it, imposing hidden information can be key. Everyone has the same opportunities at the beginning of the game, but conscious decisions by each player will affect what actions others take. So the end game will be vastly different than how everyone started, but it was the players, not the rules, that made it this way. Sometimes this can be quite effective and remarkably elegant, but it can also act as an illusion to real choices or gameplay. (Negotiation games are few in number for a reason; they are difficult to create and still give players valid choices.) There is no one genre that seems to embrace this, though many specific designers seem to, and I suppose party games would fall under this as well.
Throw it Out There, Let The Cosmos Figure It Out Many designers like chaos. Some players do, but most players want to feel like they have at least some form of control over the outcome of the game. By introducing self-balancing mechanisms--see my previous post here--designers are free to more or less throw whatever dice rolls, cards, overpowered abilities, and everything else they wish. There's no need to nitpick at the rules as long as some framework--such as auctions--causes everything to even itself out. By having reasonably minimal but critical rules, the game ends up working itself out.
Simple Rules, Complicated Components This is often found in Ameritrash and collectible card games, and my preferred method. The rules to the game should be reasonably simple, with enough to set up interesting situations but not enough that it can't be learned reasonably quickly. Then, through the introduction of different game elements--special abilities, card draws, etc.--exceptions to those rules are presented. Players have a deep, immersive gameplay experience that is very difficult to find repetitive, yet aren't burdened by a massive rulebook that has a difficult learning curve. The main drawback is that it is very difficult to release such a game and catch all of the contradictions and needed clarifications, so these games are the ones with the most errata; this turns many people off.
I am certain there are other approaches for the designing of board games, and I am interested in hearing what actual published board game designers would add to this list. If anyone has any suggestions for examples for the above listed items, I wouldn't mind drawing something up just for reference. Thoughts?