EzekielRaiden
Follower of the Way
While it wasn't D&D per se, I have used level-based "milestones" as a guide to stuff about characters I've roleplayed in other games. Spoilered, since it might get long, I'm a windbag. 
[sblock]Specifically, I created a story for a Draenei Paladin, by the name of Altuurem, in World of Warcraft that "was the explanation for" his changing specializations over the course of his advancement. Initially, he was a pretty flagrant racist (especially against orcs and elves, but at least slightly toward all non-Draenei), and also had pretty thoroughly prejudiced views on character class as well (all Rogues are dirty thieves and liars, all Death Knights are wicked abominations that should be put out of their misery, etc.) Essentially, he was a young (for Draenei) man whose youth had been scourged by the orcs' genocide of his people, then later the (Blood) elves attempting to steal their home (a science-fantasy starship), only to have to fight his way through more (Blood) elves just to get to their new home on Azeroth. So it's not like he didn't have reason to be angry and vengeful, he just let his anger control his actions and perceptions rather than the other way around.
When he hit level 40--the level at which you could get the ability to choose a second talent specialization, at least at the time I was playing the character--I wrote a story where he begrudgingly accepted orders to guard a small group delving one of WoW's dungeons, Shadowfang Keep. While there, his blind anger and refusal to see the world as it really is resulted in the whole party (in my story) being defeated and captured (he got mind controlled--a mechanic in one of the boss fights!) to be experimented upon by the archmage that runs the place. So he had ample opportunity to lie on the floor of his dungeon cell and think about how it was entirely his fault that the group would suffer a fate worse than death. However, a Horde character belonging to one of my guildmates, a Blood Elf Paladin, came through the dungeon as part of one of his class quests, and discovered the captured party. Even though their races are theoretically mortal enemies, and their political affiliations meant aiding them would be effectively treason, the Blood Elf healed them and escorted them out of the dungeon.
At this point, Altuurem's worldview had been pretty much smashed all to hell. His rage and hate had been quite pointedly demonstrated as wrong (as his teacher, superiors, and friends had been trying to tell him for months), and then a clear example of how an elf could be not only a good person, but selflessly so, to the point that Altuurem owed said elf not only his own life but the lives of his companions as well. He fell into a bit of a depression, struggling to cope with the idea that most of his sense of himself had been dead wrong and that he'd repeatedly refused chances to change. After spending a week or two in a funk, he was summoned by one of the spiritual guardians of his people (O'ros, a being of pure Holy Light energies, a Naaru), who assuaged his troubled mind and encouraged him to focus on the future rather than the past. Mechanically--and as explained in the story--he added the Protection spec (tanking), and began attempting to live up to the ideals he'd previously professed. I stopped playing before I reached the end of that character's story, but if I had continued it, he would have dropped the Retribution spec entirely (no longer needing to level grind at max level) and picked up Holy (healing) instead, fully dedicating himself to aiding others.[/sblock]
Long story short: It's not so much that EACH level means something, but I have used level break points and sudden new options as both inspiration for, and as instantiaton of, a character's story, in some games anyway. I've done kinda-sorta-vaguely similar things in actual D&D as well, e.g. building a character's backstory via interesting interactions between Class, Theme, and Background in a 4e Dark Sun game.

[sblock]Specifically, I created a story for a Draenei Paladin, by the name of Altuurem, in World of Warcraft that "was the explanation for" his changing specializations over the course of his advancement. Initially, he was a pretty flagrant racist (especially against orcs and elves, but at least slightly toward all non-Draenei), and also had pretty thoroughly prejudiced views on character class as well (all Rogues are dirty thieves and liars, all Death Knights are wicked abominations that should be put out of their misery, etc.) Essentially, he was a young (for Draenei) man whose youth had been scourged by the orcs' genocide of his people, then later the (Blood) elves attempting to steal their home (a science-fantasy starship), only to have to fight his way through more (Blood) elves just to get to their new home on Azeroth. So it's not like he didn't have reason to be angry and vengeful, he just let his anger control his actions and perceptions rather than the other way around.
When he hit level 40--the level at which you could get the ability to choose a second talent specialization, at least at the time I was playing the character--I wrote a story where he begrudgingly accepted orders to guard a small group delving one of WoW's dungeons, Shadowfang Keep. While there, his blind anger and refusal to see the world as it really is resulted in the whole party (in my story) being defeated and captured (he got mind controlled--a mechanic in one of the boss fights!) to be experimented upon by the archmage that runs the place. So he had ample opportunity to lie on the floor of his dungeon cell and think about how it was entirely his fault that the group would suffer a fate worse than death. However, a Horde character belonging to one of my guildmates, a Blood Elf Paladin, came through the dungeon as part of one of his class quests, and discovered the captured party. Even though their races are theoretically mortal enemies, and their political affiliations meant aiding them would be effectively treason, the Blood Elf healed them and escorted them out of the dungeon.
At this point, Altuurem's worldview had been pretty much smashed all to hell. His rage and hate had been quite pointedly demonstrated as wrong (as his teacher, superiors, and friends had been trying to tell him for months), and then a clear example of how an elf could be not only a good person, but selflessly so, to the point that Altuurem owed said elf not only his own life but the lives of his companions as well. He fell into a bit of a depression, struggling to cope with the idea that most of his sense of himself had been dead wrong and that he'd repeatedly refused chances to change. After spending a week or two in a funk, he was summoned by one of the spiritual guardians of his people (O'ros, a being of pure Holy Light energies, a Naaru), who assuaged his troubled mind and encouraged him to focus on the future rather than the past. Mechanically--and as explained in the story--he added the Protection spec (tanking), and began attempting to live up to the ideals he'd previously professed. I stopped playing before I reached the end of that character's story, but if I had continued it, he would have dropped the Retribution spec entirely (no longer needing to level grind at max level) and picked up Holy (healing) instead, fully dedicating himself to aiding others.[/sblock]
Long story short: It's not so much that EACH level means something, but I have used level break points and sudden new options as both inspiration for, and as instantiaton of, a character's story, in some games anyway. I've done kinda-sorta-vaguely similar things in actual D&D as well, e.g. building a character's backstory via interesting interactions between Class, Theme, and Background in a 4e Dark Sun game.