By 'leveling' I'm going to take that to be a term which encompasses the entire idea of characters that evolve mechanically, because if I look at it that way I think its easier to explain what I like about 'leveling' and why I consider it important.
I believe that at their heart, RPGs are story telling games that are most closely rooted in the make believe games of childhood. I believe that they have incorporated different concepts from War Gaming and Theater Games, but at there heart they remain more so than either of those things games about creating a story. I believe that what differentiates an RPG from a wargame or a board game or even a theater game is how it relates to the idea of a story. The very fact that D&D creates this concept called 'leveling' is indicative of the fact that its a new type of game that is going to follow from and record a story of a sort.
Almost all stories involve some concept of character development. The character is not at the end of the story the same person that he was at its beginning. There are a few stories about a persons failure to develop as a character in response to a changing environment, but typically these aren't the stories that inspire RPGs. The sorts of stories that inspire RPGs typically involve characters passing through some sort of crucible and emerging on the other side tougher, wiser, wealthier or not.
I like leveling when it reflects the evolving nature of the character, and even conversely, when the evolving nature of the character as reflected in his mechanical changes feedsback into the story and changes the sorts of stories that are supported by the game.
Now, not every sort of mechanical change necessarily needs to be the sort that D&D encourages. I'm not a huge fan of GNS theory and I have some strong disagreements with the particulars, but it is somewhat useful shorthand so:
a) In a gamist game, good leveling is the reward for a job well done. Under a gamist perspective, the level you have should in some way reflect the skill of the player. You don't see a lot of this in modern D&D, but it was a strong undercurrent when Gygax talked about good gaming. Leveling in a gamist game is fun because it means you've accomplished a goal. Good gamist leveling makes the reward satisfying - you can now do something new and exciting.
b) In a narrativist game, the mechanics represent aspects of the story so the mechanics should evolve in accordance to how the character actually changed. The concept of 'advancement' that is normally implied by terms like 'leveling' and which is critical to the gamist perspective isn't as important as the fact that the mechanics track the descisions you've made and the major events of the characters life thus far. Good narrativist mechanics force you to feel the consequences of your decisions and alter your characterization accordingly.
c) In a simulationist game, the motives of the narrativist game marry with the means of the gamist game. While the simulationist is less concerned with mechanics impacting the way he makes choices and characterizes the character, he still wants the character to evolve in accordance with what the character is accomplished. Since this is usually overcoming some challenge, the simulationist wants the mechanics to track increased (or sometimes decreased) ability to overcome challenges of the same sort. Good leveling in a simulationist game reflects how what you do reflects changes in your characters skill. Leveling here isn't so much the reward, as it is seen as the natural consequences of doing something repeatedly.
I've always thought that Chaosism CoC/BRP had the most elegant leveling of any system because it addressed pretty much all of those concerns well.
For me D&D's leveling system has made up for what it lacks in granularity for what it does to help force along the basic hero story of D&D. To me, fixing the system such that gameplay is basically the same at higher levels as it is at lower levels (and vica versa) greatly misses the point.