Thanks all for the discussion in the thread -- it has had me check my own assumptions about how skills ought to work and led me to explore down a few paths of different ways it could be done and that has been great fun!
One way I could see this working for D&D
N, written totally off the cuff stream of conciousness:
Explicitly make it such that your attributes is not necessarily ONLY your born-with physical traits, but also represents skill and development. To an extent this is already in the game -- not every 18 STR character looks like Conan -- but if most "skill" checks are supposed to be attribute checks, then let's go ahead and say "STR represents your character's ability to use their body for athletic reasons" (or something similar). So a monk who's studied how to most effectively use their body structure and mechanics could be as, or more, effective than the uber-muscular neophyte.
There is an issue with this, of course, where suddenly every archer is a world class gymnast as well, but again this already exists in the game to an extent.
With this, then many skills, such as Athletics, needn't be in the game, as your STR score is effectively that. Diplomacy could go away, as straight up CHA. And so forth.
Classes could give, rather than certain skills, a straight up bonus to a certain stat. A fighter would have a +1 to STR, making them immediately effective in striking things (balanced with whatever to hit bonus is right for a character) but also in the usual bevy of physical things we might expect, w/o being limited by low skill points or similar.
Certain Skills, or class abilities, would give straight up abilities that could work like skills. For example, being an Acrobat Rogue would give that characer the ability to make a DEX check to avoid drawing an attack as they move through the battlefield. Or being a Wizard would let you make INT checks to do what normally would fall under the Arcana skill. No bonus needed nor anything else to keep track of -- you have that ability to use an attribute roll for that purpose, or you dont. (there would be some way for non-members of that class to get that ability too)
Skills that are left could be divided up into, let's say, Adventuring Skills and Background Skills.
Adventuring skills would be specific and narrow. Climb, Thievery, Stealth would be examples -- they give bonuses or extra ability in a small range of actions.
Background Skills would be loose and broad. Merchant, Sailor, Wilderness Dweller, Performer, Clergy all would be examples. They give a small bonus to attribute rolls whenever the DM/Players agree it applies.
In all those cases (class features, adventuring or background skills) there are no specific attributes linked to it. Wherever it applies it applies. So, a fighter making a diplomatic attempt (CHA check) with a general could use his Soldier background skill to aid her as she knows how to talk within the rank, use military stories, and etc. And, when she makes an INT check to figure out how to operate a foreign seige engine, she can apply her Soldier bonus from her familiarity with siege engines in general.
So, we could have that your class gives you an attribute bonus and certain features, the theme could give you Adventuring Skills, and the Background would give you, well, Background skill(s). Or, more flexibly, backgrounds give you both a background skill and a choice off of a list of adventuring skills. Classes would likely have choices of different features, and maybe an adventuring skill or two.
I'll going to let this percolate for a bit...
peace,
Kannik