A lot of post-Forge games use descriptive attributes of some kind to define characters. These are more-or-less freeform terms that describe the character and have mechanical effects in situations to which they are relevant. A system that relies on descriptive attributes exclusively won't have a fixed set of stats. Instead, characters are "average unless otherwise stated": a PC could be given the attribute Really Strong to indicate that they're stronger than average, or you could get more evocative and give a PC the attribute Built Like A Brick House.

The key to descriptive attributes is that when and how they have an impact on the mechanics depends on what the phrase means to the group, and how the player justifies applying it to a task. The two PCs above[1. Assuming they're male, since given the gendered difference in meaning in the saying "built like a brick house", it might mean something very different that has nothing to do with strength .] who are Really Strong and Built Like A Brick House would both easily get a mechanical boost in trying to lift a fallen tree off a comrade, but the player whose PC is Built Like A Brick House would much more easily make the case that their "strength" attribute is also useful during an intimidation attempt.

Descriptive attributes are nothing new. Whether a system calls them Traits, Aspects, Qualities, or something else, descriptive attributes are a core of many roleplaying games these days. Spirit of the Century, Burning Wheel, Dogs in the Vineyard, and the PDQ system (which literally means Prose Descriptive Qualities) that powers Questers of the Middle Realms and Swashbucklers of the Seven Skies—all of these have descriptive attributes at their system's core. The commonality of descriptive attributes among successful games speaks to the robustness and usefulness of the concept.

With that in mind, consider this excerpt from Off the Grid: Using your powers in roleplaying situations from At Will:

Split the Tree

This power does absolutely nothing for you outside of a fight, right? It doesn’t have to be that way.

First, you have to buy into a different way of thinking about powers.

Powers as Personality

[L]ooking deeper into the powers you picked gives you insight to who your character is. Many people disconnect ability and personality, mechanics and story. There is no disconnect between these and in fact they often converge—if you let them.

[…]

1. Make your players explain how the power fits. Sometimes just the name of the power alone will fit the situation, but allow your players flexibility. As long as they explain how that power represents the character’s approach and mindset, everything is going well.
2. Give them a bonus. Don’t give anything for at-wills, or your ranger is going to constantly be “twin-striking” in conversation. An encounter is worth +2 to a skill check, and a Daily is worth +6. Why so much? Because the PC is going to expend that power, and if they are expending a daily power to accomplish something, they should stand a good chance of success.

That sure sounds like Powers are being treated as descriptive attributes, doesn't it? Although I do have to wonder a bit at this kind of reinventing the wheel to patch a system that supposedly[1. Not every 4e fan feels that 4e is "perfect" for roleplaying just how it is, but with all the shouting it's sometimes hard to remember that.] doesn't need any patching to support roleplaying, I would love to hear of more groups playing 4e this way.[1. That's the trouble, isn't it though? Different groups are going to like or hate this house rule, so even if you think 4e "should" be played this way you can't join any old group and expect the GM to let you use Powers that way.] Not only would it make for more interesting 4e play "off the grid", but more people playing this way can only lead to more people discovering games where "there is no disconnect between [ability and personality, mechanics and story] and in fact they often converge".

If you're a 4e GM or even just a player, go read the whole post and consider whether using Powers as descriptive attributes could add something positive to your game.