Warning: this is going to sound a bit pedantic (but everything is still IMHO and personal suggestion)...
What are skills? They represent both training and experience in a specific area of expertise. If you have the "Athletic" skill, it's because you've spent a lot of time doing sports.
But that time and experience rarely, if ever, compensates for a lack of natural talent. I, for example, love hockey and I played a lot in my youth, but the fact that I'm not naturally gifted means that reaching a certain point I couldn't go on to become a professional, no matter haw much time I put in it.
How does all this translate in game mechanics?
1) Skills (training / experience) don't replace abilities (natural talent), they compensate. Contrary to what someone posted above, if you have a 8 in CHA, you will not be a great diplomat. Ever. Your training will simply make you suck less. That means that skills should not completely overshadow abilities, i.e. it can't be an open-ended system (like 3e) where you get as good with the skill as you put points in it.
2) Skills represent your training and your experience, i.e. they are intimately linked to what you are doing at different points in your life.
Guess what? We already have game elements that represent a character's life up to the point he starts adventuring: Race, Background, Class (and level).
When you're a fighter, you don't spend points to raise your BAB, right? Class and level dictate what your BAB will be. So why should skills be different?
*Race: the skills that are "passively" passed on by your race / culture / country / whatever.
For example, Bob the Dwarf, like all dwarves (let's be cliché here), would be good with anything related to mineral resources, be it the mining of gold or metalworking.
*Background: The skills that you develop during your youth and that are related to your "civilian" life, as opposed to your adventuring life.
To continue with Bob, he's an artisan's son and apprenticed with his uncle, a jeweler. So he develops some skills in things like jewelry (obviously!), commerce...
*Class: The skills reflecting how you adventure.
Bob, after a raid by Orcs that killed numerous friends of his, decided he would get even with them (I know, still cliché...). He joins the militia to have some military training and sets out in the world as a Fighter. Bob has skills related to all things martial; for example, Bob can size up an opponent and see how much of a threat he is.
So there you have it. Bob, who's a fairly powerful fellow with sound judgment (Great STR and CON, good WIS, average DEX, INT and CHA), has a bonus when he checks for a situation relating to Smithing, or bartering. Not so much for hunting wild animals (unless he picks a Ranger level eventually...).
Try to jump over a chasm? No special expertise, straight STR roll.
Trying to repair his armor? His Smithing racial background comes up, DEX roll with a bonus.
Appraise the trading value of a beautiful necklace? INT with a bonus (jewelry apprentice).
So there you have it:
1) Turn the backgrounds into more than the (almost) empty shells they are now. They should be as developed as Races, anyway.
2) A "skill" check is an ability check, with a bonus (always the same) if something in his race/background/class applies.
That's it. Open ended, because there's not a finite list of skills. You have the background, that means you get a bonus to any rolls relating to it.
A system like this, however, requires some good judgment from both player and DM so it doesn't become an argument whether something applies every time a check comes up. Not everyone's cup of tea, I realize that.
And what about Michael Phelps? Well, cases like his represent someone who has trained exclusively in a single narrow area to the quasi-exclusion of everything else. So both background and "class" (a non-adventuring class, if there's such a thing in Next) are devoted to that area.
But to me such individuals make poor adventurers anyway because adventuring is a lot about being able to have a lot of tools to confront dangerous situations. People like Phelps are not good candidates, I'm afraid, for the adventuring life.
But that's just me...