Oblivion handled 'just by playing the game you are leveling something up' really well.
Damn I miss athletics and acrobatics :[
I sort of agree and disagree at the same time. In general, I like the overall concept of the Skyrim character system. However, perks are way too powerful (well, not all of them, but many). You end up with like 12 perks in most skill trees, and most of the skill trees border on useless later in the game without perks. Skill essentially becomes meaningless in Skyrim, except as a way to earn perk points. They need to dial back the perks, have fewer of them, and let skill level play a larger role, so that you can be competent in a skill without investing a lot of perks in that skill, but the perks do give a higher level of mastery.
I mean, you could have 100 skill in alchemy, and essentially your potions would mostly still svck without any of the perks. That's just one example, but is true for almost all the skills (except, of course, lockpicking, which you can open a Master lock with 30 skill, no perks, and a few lockpicks).
EDIT (Some additional thoughts to add clarification of what I'm driving at) - One of the things I've historically liked about Elder Scrolls games is that *eventually* you could essentially master every skill - the "Class" you chose drove your early character development, in general, so that for the first 15 or 20 levels, maybe you focus on melee, or magic, but then eventually, if you keep developing the character, you can become quite competent at everything. Since these are single player games, and you are supposed to be a legendary hero of destiny, it kind of makes some sense that you can eventually eclipse the accomplishments of lesser men/women. With the current perk system, unless I'm misunderstanding things, you can't actually ever get all the perks on one character - If there's 12 or 14 perks in a skill tree, and you can only level to 100, and you start at 20 or 30, you can only "earn" 7-8 perks in that skill tree. In order to fully master that tree, you have to "steal" perks from other skill trees (that is, level up those other skills to get more perks, but not spend any perks in that skill).
So, in essence, Skyrim violates it's own principle of "you get better at something by doing it" - because in order to keep getting better at, say, 2-handed swords, eventually you have to do *something else* to get perk points (e.g. Destruction), use the perks you earned from learning Destruction spells, to buy additional poitns in 2 hands. So you are exactly NOT getting better at something by doing it.
END EDIT.
I might be a minority here, but I also miss the character attributes (strength, speed, luck, etc). I liked the fact that I could increase my carrying capacity very significantly with potions and enchantments (I mean, you can somewhat in Skyrim too, but it's much more limited).
I miss teleporting, jumping, and levitating from Morrowind.
I miss the "Open Lock" spells. If I'm playing a mage, sure I *could* learn lockpicking, but I'm a mage, dammit! If someone wants to roleplay a theif, let them use lockpicks. Let someone roleplaying a mage use spells.
I miss destruction enchantments on amulets (which, in Morrowind, played much the role that staffs did in Oblivion and Skyrim). I sometimes enjoy playing a spellsword or battlemage, but I think it's stupid that enchanting, which is basically a mage skill, favors melee fighters (because you can enchant a destruction spell onto a weapon; but you can't enchant a destruction spell into an amulet or staff to cast at enemies as a pure magical attack to supplement your magicka; yeah, it can become OP - it pretty definitely was in Morrowind, but that could have been balanced; and yes, in the end, magicka cost reduction enchantments can play much the same role, by allowing your character to cast their dusctruction spells a lot more times before running out of magicka, but still).