I often put out sponges in water with a little bit of baby soap in it on Fridays in my room and let the kids clean the tables, chairs, shelves, and toys. Obviously, this is not a replacement for regular room cleaning, but it stemmed from their interest in watching teachers cleaning tables, toys, and other things during the course of the week., and asking to help. Sometimes I put out little squirt bottles (with just water) and rags for them to clean with since this is what we actually use; I tend to do this in the summer since the fans are running and windows open to help dry out the excess water (and we can escape outside while it does dry).
There are plenty of benefits to this activity- pride and sharing in responsibility in their classroom, gross motor development, and learning words like "wring," but importantly, the children really enjoy doing this, as they enjoy mimicking many other activities that adults do. I also keep little hand sweepers in the room for them to sweep whenever they want but also to sweep up spills from the sensory table or little pieces of paper at the art table, etc. (Generally, I do not make them sweep things up, but when they are done I ask them if they could help sweep up (they usually are excited to do so) , if they say they don't want to then I "help" sweep- meaning I sweep and they come to my aide as much or little as they want to).
The next activity is new to my "repertoire," after I had a child ask to use my hole punch and then several others wanted one too. I bought several hole punches and left them out with colored scrap paper and let them go to town. They seemed happy enough just to punch holes for the sake of punching, and I kept the "dots" they didn't want for collages, etc.
While they just enjoy this activity for its own sake- it is also a very practical activity. This develops hand muscles and coordination needed for writing and cutting. A child, who had just been using the hole punch, and then started to use the scissors, said to me "scissors easy after the hole puncher." Sometimes I wonder if they read my mind. :-)