This suggestion share some elements with other hobby suggestions, but I feel it's different enough to warrant a new thread.
I propose a change in the function of the mayor from occasional meeting holder to dwarf interviewer. (a more full time position)
Once the mayor position opens up, a new screen is available; The dwarvish message board. The mayor systematically interviews all the dwarves, and occasionally one with generate a request; These requests would be quite mundane and specific in nature, Appearing in the form of "(Dwarf) Request (Object) to (Process) For (Motive)" i.e. Urist McReligion requests a stone bolder to carve into a statue for personal warship or Urist McSweetheart request a necklace to give to his wife to mark the 20th anniversary of her being attacked by a honey badger in OffSite. There is no penalty for ignoring these requests (they can even be deleted off the board), but fulfilling one only required a few button presses (to select the exact bolder you want to let Urist have) and generates a happy thought. Once a request has been filled, the dwarf stops their current task back on the que, retrieves thier granted object, uses it for the requested purpose, and goes back to work with their break and sleep timers reset.
Dwarves could also request materials for a hobby; "Urist McNinja requests a sword to practice with" or "Urist McIndustry requests 10 stone boulders and a table to practice carving with". A martial request would have a dwarf take the given weapon, carry it about, and when they go on break they would have a high chance(Based on personality) of going to their room to do weapon drills. A crafting request would see a dwarf take a table and set up a special 1x1 workshop in their room, assuming they have space. The dwarf could then spend breaks in their room using the equipment; Objects would be produce at a very slow, non-increasing rate, would not consume any of the resources allotted, and would be the personal property of the dwarf who made them, to keep or give away as they please. Hobbiests would gain boosted experience to make up for their painfully slow production rate.
The function of this mechanic would be to breath more life into individual dwarves, and give RPer something more to base their stories off of, and to give optional lategame goals to players trying to run a utopian fortress.