I had some good, thought provoking comments to my Klondike Bar post the other day.
When I said that I think for D&D a character only needs a desire to explore the world and get rich through looting tombs/battling monsters, I do only mean that as a part of character creation.
Once the dice hit the table, characters should begin to be fleshed out by actions that happen to them within the game, choices the players make for them, and goals the players set for the characters themselves.
A few examples from past experiences I've had, both good and bad.
1. My first D&D character to make it to 2nd level, Gwydion (hence my internet alias), about the time he hit 5th level or so, decided his goal was to purchase a longship and crew so he could return to the Isle of Dread any time he felt like it. The first time we played the module, we didn't have any ships among our characters, so we used one of the provided hooks of a loaned ship. I wanted more IoD fun for my character, so my short term goal became to save enough for that.
2. My brother Tim's main character was a Dwarf named Larry, and when one day he rolled up another Dwarf as a replacement character for one that died, he named him Gary and said the two were brothers. Because of the TV show Cheers, where the rival bar was Gary's Olde Towne Tavern, Tim decided that the Dwarven brothers were going to open their own inn rather than build traditional strongholds when they hit name level. If one other character hadn't died, we might never have seen that brother appear, and this all never would have happened.
3. In a mixed 1E/2E game with the Evansville group, I was running a Dwarven Fighter/Thief. Due to very poor rolls by me in combat, compared to very good rolls by certain monsters, my guy was always getting knocked around in combat to comic effect. I ended up changing the way I roleplayed him because of that--originally he was a gruff but honorable trapspringer. He ended up being more of a willey, dastardly anti-hero just because he'd learned that fighting fair didn't work for him.
4. In one of the many short-lived 3E games with the Ebisu Group, we had one game where we started at 10th level with 2 characters each. I'd written up linked backstories for my two characters, a Half-Orc Rogue and a Human Ranger, who were half brothers, sons of a famous human Bard and members of the same Thieves' Guild. The first encounter with giants and a Pit Fiend sees my Ranger biting the dust to some uber save-or-die spell, and there went all that hard work within 30 minutes of starting the game.
5. In Paul's BECM game with the Yamanashi group, I rolled up a Magic-User who had all scores average or lower, except an Int of 13. I took Charm Person as my first spell, and lots of various equipment for dungeoneering. Using those scores, I made him an offensive braggart (low Cha) named Valentio the Pungent who lorded it over all the other characters how much smarter he was than any of them (because a slightly above Int was all he had to work with!). I never would have come up with a character like that if a) we'd been playing with a high rolling method like 4d6-L, or point buy, or whatever, and b) the way things went in the first adventure, when I was using some smarts and gear cleverly in ways most of the other players, who hadn't been playing as long as me, never thought of.