I usually don't care much for those desktop pet things. I had a Tamagatchi once. It died in 3 days.
But DF related one I could live with. If you are looking for ideas, I got A small little room with a waterfall pump that you manually crack by clicking on to make yer dwarf happy, clicking one lever will drop food down into his room, clicking another will add booze. and he'll wander his little home. Entertaining himself by constructing and deconstructing little sand mini structures in his own little sandbox.
Of course he would need to be able to randomly trap himself behind walls while in the sandbox, and would need your assistance to save himself from his own stupidity. Punishments could include spawning a vermin in his room that will bother him for a few minutes, sealing the waterfall drainage for a few seconds to flood the room just long enough to panic him, letting the hammerer in, and flooding the room with magma for a few seconds. All but the vermin has increasing chances of death. If he gets too unhappy he goes melancholy and jumps down the waterfall drainage, creating a nice random miasma cloud for a few days later. All levers and buttons will be unlabeled.
P.S. And as a side note that link set off all kinds of red lights and warnings from my Mcafee, everything from trojan downloads to adware to that PITA doubleclick.net cookie.. I'd be careful what you download from there.