The way Toady One made every dwarf unique and added in those little personality bits really affects the way I play and view the game. I know that they probably don't do much as of now, but when I choose people for administrative tasks, I always check their personality traits to see whether they would work in the position.
For example, I was thinking of assigning a Captain of the Guard, so I went to my military to see which dwarf would be suitable. I find a speardwarf with what I felt were very good personality traits to be the Captain of the Guard.
She's got the mindset, she's ecstatic, seems to have friends from her constant sparring sessions, so she's in. Now, a few seasons later, I check on her on a whim, and the list of her thoughts is now jarringly empty. She's content, been comforted by a pet and has been in the rain. Naturally, my imagination works overtime, and I fabricate a quick life story of Udib Tabarfikod.
"Beginning her life as a novice miner, she was drafted one day to deal with the raccoons that were pestering the dwarves outside. Understandably unhappy about being drafted, she nevertheless kept an open mind. She found that defending dwarves from fearsome wolves and irritating raccoons gave her joy, and that sparring sessions invoked the dwarven exhilaration of combat in her. She was transferred into the hammer-wielding Kel Gongithonul's squad after proving her skills with the unadorned steel spear, and quickly became close friends with him. The small squad of Gusilkonshoras was known throughout the fortress for having the highest success rate in dealing with thieves and savage beasts, owing to the effective maneuver that Kel and Udib called, "Hammering the goblin into Udib's spear." One day though, Udib was interviewed and deemed fit for the job of Captain of the Guard. After her promotion, although her position as subordinate to Kel in the squad stayed the same, she was given a office, dining room, and larger housing quarters to herself. This subtly changed the way in which the other members of the squad treated her, and she found herself growing farther away from the previous camaraderie of the squad. Although she felt regretful, and sometimes resentful that she was appointed the Captain of the Guard, she believed that working towards the good of the whole fortress was a righteous and honorable job, and continued to invest much of her time in her work."
I tend to get a lot of these random life stories popping up in my head thanks to the implementation of personality characteristics in Dwarf Fortress, so I think the small stuff really tends to differentiate it from other games. Would this be considered emergent gameplay? Haha, but anyhow, my point is that Dwarf Fortress is awesome.