Wanted to add that in my dream scenario, magic items still matter, which is why items/enhancement bonuses are excluded from the non-stacking. Also, I hate magic item Christmas trees (in other words, a slot for every magic item, and a magic item for every slot) or the need to have items to keep up.
Also, I want the math to be such that every new item truly is a treasure. For example, if a fighter finds his first magic sword, say at level 7, he is just as excited at the +1 enhancement bonus (which stacks with his current attack bonus) as he is the increased crit damage and at-will sunrod property. This is because the player likely has already found all the existing attack bonuses that are available to him, and any additional increases in accuracy are very, very rare.
I might place his next sword somewhere around level 16, but this time it's a +2 Flaming Sword. It replaces the previous +1, and now his sword gives him a bit of extra fire damage and a total 10% increase in hit chance. He's excited about it, but the math scales in such a way that he doesn't need it, and the game does not require that he have it.
For skills, I imagine my drow rogue, who wants to be super good at Stealth. Let's say he starts with a +5 Dex bonus, obviously has training, and even got Skill Focus: Stealth (+3 being a bit greater than the +2 racial bonus he got for free). He topped it off with camouflaged clothing, a mundane item giving perhaps a +2 item bonus. Assuming that training gives a +5, the drow has maxed his Stealth check at +15, and will have a very hard time increasing it (except for ability score increases, which will take awhile). Under my system, he will pass the hardest checks (around DC 30) only 30% of the time, so he still isn't quite satisfied. So, when he finally finds that Elven Cloak (+5 item bonus to Stealth), he will probably be very excited to replace his mundane camouflage with a much better magical item. And the math still isn't broke, since although he'll pass every mundane Stealth challenge quite easily, those things that should be a challenge even for the greatest sneak ever still will be (+18 vs DC 30, 45% chance of success; after a few ability bumps, he'll finally be better than a coin flip).