I don't think a truly stat-less system is a good idea for a CRPG, although probably interesting for MMORPGs or P&P.
In real life, a person generally has a fairly good idea of how good they are at any given task, assuming they've tried it before; and since they live every moment as themselves, they have tried a good many things. They have no need to keep some record of their abilities, because it's instinctual.
However, in a CRPG you are going to be playing a character for, say, 40 hours. Moreover, character development is part of the appeal of the RPG genre, so rate of time flow and thus stat development is necessarily faster than in real life. To complicate matters even further, a player may only play the game for an hour or so every couple of days.
For all those reasons and more, I believe a CRPG requires an in-game record of character abilities. However, this stat sheet doesn't necessarily have to be numerical or exact. One interesting system is used in the MUD The Eternal City. In that game, stats are represented internally by the system as a number (of course), but this isn't visible to the player. Instead, they see a word ("average," "abysmal," "quite good," etc.) that represents a broad range of numerical values. These ranges aren't uniform; although players aren't told the actual distribution, it appears to be fairly Gaussian, so that the "average" category encompasses the broadest range of numerical values, and the most extreme (good or bad) categories encompass the fewest. Similarly, when they train stats (on, for example, an obstacle course) players can tell that they're improving a stat, but can't tell by how much (this varies randomly). This is similar to "feeling the burn" after working out, but not being sure how much you have improved your strength. It is generally more difficult to train stats the better they are. What this system ultimately accomplishes is that the player can see at a glance what his character really ought to know: broadly, how well suited he is to various tasks and how he compares to others.