I have devised a magical way to deal with so many of the problems with skills, but still keep a semblance of them because, dammit, we want our characters to know things and be different.
Primary and secondary classes (and tertiary, probably). Primary class = this is how I kill things. Secondary class = this is how I interact with people and the world around me. Everything that we would currently put under skills would go to your secondary class choice as well as non-combat class abilities.
The secondary class would give you a certain amount of things that you sometimes succeed at and a certain amount of things you always succeed at. Maybe these are chosen from a limited list for that class, maybe the only choice is which class you take. Some classes have a lot of sometimes but no always. Some classes have a few always, but almost no sometimes. In addition, the player would be encouraged to describe their ability in the way that makes sense for them. Open locks could be picking it with little tools, or it could be a whispered spell, or even a stroke of magnificent luck.
The best part about this system is that it would give you the ability to truly make that character you envisioned. Want a sneaky wizard? Magic damage and roguish skill/ability set. Want that nobleman? Fighter damage and aristocrat skill/ability set. Want the tricksy guy who knows some charms? Roguish fighting with a magical skill/ability set.
The best part is that the combat class offers virtually nothing to noncombat and the noncombat class offers virtually nothing to combat, making all combinations equally valid, equal in power.
Making the character starting from higher level wouldn't be too tough. Every level, choose the combat ability you gain, choose the noncombat ability you gain, write down the automatic abilities you gain then pick a feat or an ability increase if you get one that level. Fairly easy but complex enough to suit a nuanced game. I envision feats still being around, but you'd have to decide to spend your one feat on something for only one of your classes. This is where the campaign-specific differences come in. For a one-off game, take all those combat feats. If you're playing in my weekly campaign, I might suggest a goodly amount of noncombat feats.
In keeping with letting the player choose their own fluff, I want the skill-type abilities to be more general. Academica: Stuff you learned in school, or maybe that your summoned imps tell you. Geometry, Astrology, History, etc. Getting There: Any check in a situation that involves getting from here to there. It might be acrobatics, athletics, jump or climb as long as it involves moving from one spot to another, but you can describe is a ninja leap, a teleport or turning to shadow and slipping over. So the skills/abilities are more about the type of result than the method to obtain a result.
Now, how do I get all my ideas to Monte?