Magic Items whose effects vary depending on wielder stats of some sort

[Jowgen]

I know about Staves, which are expensive wands that let the wielder use their own CL for dependent effects

What else is there?

[elonin]

Runestaves. These are not charged items, though.

[Rubik]

The psychic weapon property, in the XPH. Adding it to a weapon increases the enhancement bonus the more power points the wielder has.

[avr]

A lyre of building depends on your perform skill to continue use past the minimum amount.

[Necroticplague]

There are some magic weapon properties that have their DC set by your CHA mod, like a spell.

[Rubik]

The psychoactive skin of proteus may have a flat ML of 7, which means the forms you can take don't vary, whether you're level 1 or level 21, but the forms you nab do better the higher your (non-physical ability) stats. Your BAB makes it easier to hit, of course, and your mental stats can heavily influence the DCs on some of the abilities you get access to.

Complete Psionic allows you to use your own power points to manifest powers held in power stones at your own manifester level (and allows you to augment to suit), meaning that a 25 gp level 1 power stone of Inertial Armor gets a lot more mileage at ML 21 than ML 1.

Many low level spells scale with level, so spell storing items (such as spell storing items, rings, or glyph seals) do better at higher CL.

Metamagic rods do the same thing at all levels, but stronger spells get more out of them. Empowering a CL 10 Fireball gets a lot more dice than a CL 5 one.

[Shalist]

This isn't quite what you're looking for, but perhaps its worth a mention. There's the non-epic enhance item feat:

Choose any item creation feat you already know. When you create an item with that feat, adjust the DC for saving throws required by the magic item, if any, by your key ability modifier.

That's plenty useful in and of itself. Apply it to one of those Eberron cost reducing feats (legendary / exceptional / extraordinary artisan) to avoid having to choose a specific item type.

Apply it to all 3 for 3x your ability modifier thrown on top of whatever DC the item would normally have had. And if you've really got too many feats laying around, just remember that 'enhance item' is itself an [item creation] feat...

Enhance item: (Enhance item: (Enhance item: (Legendary artisan)))

edit: I was wrong about it adding to the normal DC rather than replacing it, so no self-stacking and what not.