I don't want characters defined by their magic items. Yet I want magic items to be powerful relative to character abilities.
I know there are a lot of people critical of D&D because, as they put it, characters are defined by their items. But I consider that a bit of a misplaced analysis. Items have always been an important balancing factor between martial classes and spellcasters, no doubt about that. But aside from a few iconic cases (paladins with holy avengers or PCs with a particularly juicy item like a vorpal sword or flying carpet), I never had the impression of a PC being defined by his items before 3e.
I think 1e/2e didn't give me that impression because, although some items did have a significant impact (notably carpets of flying and cubes of force), as players we weren't really in control of the item placement process. That was the DM's job. We didn't have (or take) any ownership of that process. It didn't dominate our plans for our PCs. There were notable exceptions when questing for particular items, but those were relatively rare.
Contrast that with 3e's magic item creation and magic market assumptions. At that point, players started really taking ownership of what their PCs had and devised schedules of regular upgrades as the wealth rolled in (according to appropriate guidelines). Those of us who ran 3e games like we ran 1e/2e games, probably still didn't see huge issues with items defining characters. But for those DMs and tables who pursued the new assumptions, perhaps even seeing the WBL and item values as a system like point-buy super power buying in Champions, probably developed the impression of items defining characters most.
But even in 3e, thinking of characters as being defined by items (particularly the simple bonus items) is a fairly shallow analysis. Most item bonuses were small relative to inherent character bonuses derived from stats or class, with AC as the single prominent exception (and let's be honest, how many characters define themselves by their armor protection? Few!). A 15th level fighter may have a pretty sweet +4 weapon and a belt of giant strength +4, but the +4 he gets from the sword and +2 from the belt are exceeded by his +15 from class, +2 from feats, and +4 from his inherent strength. No doubt the extra +6 from equipment helps when fighting at the high end of his opponent spectrum, but the initial +21 is probably necessary to even tangle with the low to mid range of his opponent spectrum.
What I want out of D&D Next's magic items is a renewed sense that items are not regular power-ups on the route to higher level. I want a renewed sense that they are not an entitlement but a reward, usually serendipitous, for adventuring and surviving. I want a renewed sense that players can't safely plan for particular magic items unless they play through quests for obtain them (though I accept that payment in advance is also acceptable as in the case of Perseus being equipped with magic items in order to accomplish the quest of killing Medusa or Frodo being equipped by Galadriel to sneak into Mordor).