I always do their requests because I want the pictures. However, I really regret giving Stitches a fossil piece because he's slapped it in the centre of his home. ): Hopefully he removes it or asks me to buy it off him again.
The exact same thing happened to me!
I've been more strict about villager requests; if it's a fish or a bug then most of the time I flat-out refuse. Especially if their house already looks like a zoo. It took me quite a while to restore Roscoe's house to something that looks nice and actually habitable.
But I spoil them with any other kind of requests. I've stockpiled a crapton of perfect fruit just for the occasion...