Running and Swimming are two different skills, why not have a character that is athletic but can't swim very well?
The language skills aren't necessarily useless when implemented well.
I would like to see more crafting skills in addition to alchemy (cooking, sewing, smithing, enchanting)
And some optional hidden skills that remain locked until you learn them in the game (like necromancy and a martial arts style that replaces and improves unarmed)
Magic should have eight schools instead of five.
Thaumaturgy (levitation, feather, detection)
Alteration (shields, unlock, sharpen blade)
Illusion (light, chameleon, earwig, ...)
Destruction (...)
Mysticism (...)
Restoration (...)
Necromancy (turn undead, reanimate corpse, ...)
Manipulation (charm, sleep, wake, frenzy, ...) -> charm has nothing to do with light or sound, it's manipulating someones mind so it should be a different school.
Even if you (not you specifically Obxure) didn't like the idea of removing backward running, how is the dodge skill different from the armor skills? If you aren't going to be hit at all because of your player skill, then remove the armor skills.
I like having eight magic skills, and bring back Thaumaturgy is a good one. Necromancy would also rock. I'd prefer though to eliminate restoration to add those spells to thaumaturgy. Necromancy would be an intelligence skill like medical would be, so it makes a better pairing for them to employ that instead (not instant healing of course). I don't really want to see the game letting you chug health potions all day or keep casting healing spells on yourself, so I'd like to nerf Restoration quite a bit.
Schnell Olfy suggested replacing alteration with a school called Dynamism that uses alteration's "Force" type powers, like shield, open, burden, feather, and take telekinesis from Mysticism. It seems like a better grouping of abilities to me. Water breathing and water walking would return to thaumaturgy.
I'd like to replace Conjuration with the Daedric skill, letting you summon daedra but not undead or wildlife.