I get most of my enjoyment out of DF by roleplaying with it actually.
That includes community forts obviously, but even forts I keep to myself I like to RP the scenario. As an example, my current fort is a highly militarized fort under the pretense that it's supposed to be a sort of front line defense against the evils of the world (it's modded, so no goblins, but you get the idea). I've tried to set up a realistic command structure, starting with my expedition leader / major, to captains of the three companies, their lieutenants, sergeants and ultimately privates. Dwarves are stupid though, so it doesn't work that way, but it's fun to imagine it does.
In my community fortress I played it up as a mining town, where I set challenges upon myself to export lots of iron and steel. There were also relatively few attacks because I only had the equivalent of badger men around, which made deaths and injuries more dramatic. In a community fort where I was a player, I picked a soldier who migrated with only her daughter (her husband was MIA and presumed dead, .31.25), who died several years later when she tried to defeat a forgotten beast alone to defend her honor. Lots of potential there, which I milked a bit too much perhaps.
DF gives lots of opportunities for interesting stories like this. You can make almost anything out of the various associations between a fort's citizens as you want. From them losing friends and family to doing things like killing a baby snatcher 1-tile away from the map edge or opening a floodgate during an experiment and drowning a lot of people, there is pretty enormous story telling potential.