I've come a long way from rolling into Riverwood as a fur-armored ex-convict loaded with cheap loot. My character is now a level 42
I can't believe I only touched on the leveling system last time. The leveling systems of Morrowind and Oblivion were deep, rewarding, and multifaceted, but also quite flawed. The system of major/minor skills in Morrowind and major skills in Oblivion meant that when you created your character, besides choosing your name, race, birthsign, etc., you also picked a subset of skills your character was especially good at. You would advance more quickly in those skills, and increasing a total of 10 of them cause you to level up. Except your total skill gains also controlled the possible attribute bonuses you received upon sleeping to level up, and you could only pick three, and if you had too many bonuses you'd waste some of your skill level ups, and if you had too few you weren't gaining attributes fast enough, and you had to devote one of the bonuses to luck almost every level if you wanted to maximize it, and you had to maximize endurance quickly by leveling Armorer, Heavy Armor, and such to maximize your HP...
As you can see, the leveling system of previous games was a mess. The major skills were the ones you were supposed to be good at, the ones that defined your character's archetype, but you wanted to make them skills you wouldn't be leveling, at least not naturally, because then you wouldn't be able to precisely control when you leveled up to ensure you always gained the right amount of skills to maximize your attribute bonuses. If it sounds confusing, that's because it was; I had to get mods to "fix" the leveling system and keep myself from having to obsess over which skills I was leveling when. It was nasty and seriously broke the immersion of the games (at least for calculating players like myself) by keeping you from playing your character "naturally".
The leveling system in Skyrim, then, is probably its biggest improvement. I would say it's even better than any of the mods of the previous two games. Basically, there are no major or minor skills anymore; all skills count towards your next level, though higher-level skills (the skills your character is best at) count more. Makes sense. Also, as I mentioned before all the attributes (strength, endurance, intelligence...) have been removed; health, magicka, and stamina (which also controls how much you can carry) are now your character's only attributes, and rather than bizarrely tying their advancement to your skills, you simply pick one to increase by 10 whenever you level up. Total control. You can increase mostly health and stamina for a beefy fighter character, or more magicka for a mage. Just being able to do whatever I want, increase whatever skills I want, actually leveling up a diverse variety of skills willy-nilly, is tremendously freeing, like the way The Elder Scrolls should be. The birthsigns and specialties of previous games have both been folded into the guardian stones; rather than picking them once at character creation, you choose a guardian stone and can switch at any time by visiting another stone.
But even with no specialties or major skills, you are still encouraged to specialize your character; it just happens gradually as you play the game and explore, rather than at the outset when you barely know your character yet. This is made possible by the "perk" system, which is almost as brilliant an improvement as the skill/attribute system was a fix to previous games. Basically, every time you level up, you get a perk point to spend. Each skill has its own tree of perks to explore and choose from; as you increase the skill and go deeper into the tree, more perks become available. Simply increasing the numerical value of your skills is less powerful than in previous games; to really get good at a skill, you have to get the perks of that skill. These range from greatly increasing the effectiveness of a skill beyond what simply increasing it could do, to nice little bonuses (the chance to critical strike with sword attacks) to awesomeness. (Having two summoned minions at once) It makes leveling much more dynamic, interactive, and all-around fun.
Update: My level 51 character (now the Archmage of the College of Winterhold) has maximized his smithing and enchanting skills. He has fully moved into a three-floor mansion in Solitude, the seat of Imperial power in Skyrim. I've killed enough dragons and captured enough souls to finish his legendary, double-enchanted Dragonscale armor that boosts his stats, lets him resist elements, and lets him cast Destruction spells for free. Yes, spamming the expert-level Thunderbolt spell is tons of fun. Amazingly, though, even with that and my infinite-charge Legendary Daedric sword that does fire damage, the game still has its challenging moments. This game is amazing.