Without getting into rules changes and focusing only on the tropes of the game, I'd concentrate more on influences from mythology, folklore, and fairy tales as opposed to fantasy novelists. There'd be less Tolkien, Vance, and Moorecock and more Homer, Chaucer, and Virgil. I don't just mean races and monsters, but the very mood of the game. There'd be more mystery with regards to how the world works, more room for players and DMs to add their own creative spark. Monsters and races, for instance, would be more than a description, picture, and stats. They'd each have a thematic element to it. What does it mean to encounter a dragon, unicorn, or other spectacular creature? What does it mean to include non-human races into the campaign? These are the sorts of things that really add dimension to campaigns, not reams of maps and microscopic details that sometimes hint at a larger idea.
"Adventuring" would be more like questing and less like a way of life. Of course, some quests take a lifetime to complete, but the general idea is that I want to get away from the mercenary standard set in the core rules that masquerades as heroism.
The characters' personal strengths and weaknesses would have as much--if not more-- influence upon his fate as their innate capabilities like Strength, Dexterity, HD, etc. As the rules currently stand, you are more often penalized for thinking outside the wargaming box, even if you create a character known for being courageous, compassionate, wise, or what have you.
The rules would be more like a toolkit than a prerequisite for gaming. This bears some explanation. I realize that some rules are necessary to play the game, but I'd prefer a simple base mechanics with options for more mechanics-intensive play.