I love chess, at least conceptually. I’m not a very good player, but as a bottomless bucket of metaphor? Fantastic. But I sometimes bump my nose against its perfect symmetry. Not to say that’s a failing of the game, but it means chess can’t tell certain stories that an asymmetrical game can.
An asymmetrical game is one where both sides have an even shot of winning, but different resources and sometimes even different rules. A game of Magic: the Gathering is somewhat asymmetrical, but not very. The new Archenemy decks (which gives one player a bigger, more powerful deck and pits him against several opponents) is a better example.
My favorite is probably Fox & Geese, a checkers variant I learned as a kid. One side has 4 pieces that move normally (the geese), the other has one piece that can move like a king (the fox), and the fox’s goal is to get to the far side of the board, while the geese attempt to pin him. To a kid, it seems like a lopsided game – the fox seems way too powerful – but with experience, the potency of the geese are revealed. It’s not a game with huge replay value (though kids like it) but it’s a wonderful illustration of principal.
Symmetry vs. Asymmetry is a conflict that doesn’t see much play because it’s not terribly dramatic, but it’s a subtly potent one, and one that’s worth looking at in character creation in RPGs. For illustration, I’m going to compare D&D 4essentials vs. Gamma World. Both games use template selection as the basis for character creation. There’s a bit of a distraction with generating stats (which Gamma World cuts to the heart of quite effectively), but it’s just that; a distraction. The reality is that you combine a few elements. For D&D it’s Race + Class, for GW it’s Template + Template.
The difference that stands out is that in D&D, the choice is profoundly asymmetrical. Your race contributes a few bits and pieces (mechanically) but the meat of things is in your class choice. Certainly, some of those racial pieces may be essential to your concept, and that’s fine, but the choice of race sways things less than the choice of class. That is to say A dwarf Knight and an Elf Knight have more mechanical similarities than a Dwarf Knight and a Dwarf Wizard.
This is not a criticism, by the way. D&D classes are sufficiently complex and full of choices that you would not necessarily WANT race to be more complicated. If race had the same mechanical depth as class, character generation would be way more complicated than could possibly be considered. However, there are some tradeoffs made for that model.
Consider, in contrast, Gamma World, where the character is created from two symmetrical templates. While the templates vary in color an content, they are similar in structure and capability. This means that character creation is a simple matter of taking any two templates and smashing them together. This is fast and easy, and has some incidental benefits – it requires only one random table, and it means that each new addition expands the range of possibilities more effectively – but it also demands a bit more mechanical simplicity. For the same reasons that D&D classes can be complicated, Gamma World templates need to be pretty straightforward.
Again, it’s not a condemnation, but it’s a consideration – both approaches have strengths and weaknesses, and which one is better suited to a particular game is something that it’s worth thinking about. Consider that it would not be hard to re-imagine D&D so that races and classes are symmetrical, but it would mostly be done by simplifying classes, thus changing the nature of the game.
Now, I’m nuts for combinative template systems. The speed of templates combined with the flexibility of interpretation that combination allows tends to make for some really solid, inspiration ideas (including my long standing favorite from a game I ran, Cowboy/Ninja/Diplomat). It’s one of those ideas that I wish more games could support, but which hits upon unexpected rocks when you try.
See, you can theoretically make templates for most games, but you’re likely to bump up against the vagaries of point buys. If the game has progressive costs (first point costs 1, second costs 2 and so on) then it’s hard to say Template 1 gives you two ranks and Template 2 gives you three ranks because that’s 5 ranks for a cost of 15 points that you got for 9 points ((1+2) + (1+2+3)). Yes, you could abstract it further and say you get whatever 9 points buys, but that wastes 3 points, at which point your attempts to come up with a fair way to handle the extra points undercut the whole point of going with templates. 
The trick is that a lot of games handle addition badly (Fudge/Fate’s especially bad at this) and break quickly if one character ends up pulling Kensai and Duelist or some other combination that piles strength on top of strength. All to say nothing of weird fiddly bits, like when two templates both have the same (non stacking) advantage or if one has an advantage that impacts the cost of something else.
All of which is to say that you need a system which gracefully handles addition (which, for example, Run Out The Guns did) or which, like Gamma World, decouples the templates entirely. That is to say, like most 4e games, there’s a thin rail of a system where your character has hit points a basic attack and a normal set of actions which everything else is layer on top of. By layering on entirely new material (that is to say, new powers) and minimal modifiers, there’s no way for the templates to trip over each other. There may be some combinations that offer more or less interesting variety, but none that break the game. Not only is this useful now, it’s useful as new templates get added (because of COURSE they will) because they’re harder to break the system with, and you don’t need to stress out as much about every possible combination. Design the template well, and the combinations take care of themselves.
Now, my fondness for combining templates may be a bit more enthusiastic than average, and it may be a bit extreme to wish that EVERY game supported them, but it’s definitely an idea that could see more use to good effect.
1 – D&D does often offer a third choice for style, and I’ve written about how important (and poorly supported) it is, but practically it’s a subset of class choice, especially in Essentials. Effectively there are two different “Cleric” classes, for example.
2 – It would also still be Column A + Column B. Until you find a way to allow a Dwarf/Half-Elf character to make sense you can’t fully combine them. Not that it’s impossible, especially in 4e, but it’s a bit of a leap.
3 – I cannot tell you how much time I’ve beat my head against this with tri-stat, and it never quite works, which is a huge shame since if it did, it would be a thing of beauty.
4 – ROTG was built on top of Rolemaster, which is very addition tolerant, in part because the diminishing returns are built on the far side of the point buy. That is to say, ranks 1-10 increase your skill by 5 each (it’s a percentile system) , but 11-20 increase it less, maybe 3 each – it’s been a while and I forget the numbers – and so on. Net result, a big addition spike doesn’t actually break anything.