I, uh, totally did the one pertaining to the 22nd yesterday. Totally.
There is no reason to distrust me in this moment.
So, anyway, let's talk about non-dice systems that I like.
(questions and image from autocratik.blogspot.com)
One of the things that I really like is when players have a connection to elements in the world. This is a little bit of a cop-out, because I'm going to mention a couple specific systems, but I think you'll understand what I mean when we're done.
In Smallville and other Cortex System games, there's a system where your relationships give dice, and while I think it's a good system mechanically it also uses dice, so that's out. However, we can still look at Degenesis and Shadowrun as having some similar systems, and even Eclipse Phase for that matter.
What Degenesis does is instead of having classes and races, you have cults, which reflect a society that a character can join. When characters have a certain set of skills and abilities, they advance in rank, earning new perks. Sometimes these are mechanical, but they're often really narratively interesting.
I like these because they allow the players to have a defined role in a way that aptitude-driven things don't. I'd also like to point out Paranoia, with its defined squad roles, and 13th Age, with its Icon system, as games that have similar concepts, though perhaps not quite in the same direction and style as those of Degenesis.
Shadowrun and Eclipse Phase both have systems to measure contacts, and in Shadowrun they are more simply mechanical (I actually thought that a system like this was basically standard in games, until I played other games and figured out that it wasn't), but in Eclipse Phase they're more overarching setting constraints because characters develop ties to factions through reputation networks.
Systems like these are nice as a designer because they're something that encourages play within a certain set of rules without mandating it, but they're also nice for storytellers because they lead people in a direction that is relatively predictable, which is not something that can always be said for other systems (of course, a good storyteller gives the right hook and plot to interest their players, but that's a process of communication and growth, not just magic intuition).
The big thing that's nice about Eclipse Phase or Degenesis in particular, with their focuses on factions, is that players can inherit a lot of the ideological affinity of the factions they choose for their characters, or set their characters up as iconoclasts. That adds to the dynamics of characters without requiring a whole ton of foresight on behalf of the players.