The worst critters in my basement are crickets. My little cat will chase them down and eat them. Sometimes I just find the legs. Yuck.
I don't have crickets, but we literally have box elder bugs crawling out of the walls. Our previous home, did not. I think it's the sprayed cellulose insulation. Luckily, they don't damage anything. They are just there. Like with the crickets, my cat will sometimes eat the box elder bugs, after toying with them a bit. Our dog will also sometimes eat them. Usually they'd only come out when the weather would warm up. However, we still have some coming out, and it's been below zero.
When I had my studio in the basement some years ago, my cat used to leave foot prints in my platters all the time. And one day he jumped up onto a shelf that was filled end to end with 180 bone dry votive candle holders (for our wedding reception). He walked from one end of the shelf to the other by putting his little feet inside the pots, then jumped off without breaking a single one.
Fun fact, cats can alter their body weight based on the surface they are standing on. I'm fairly certain they can walk on water, and even pull off some of that "Crouching Tiger" air walking stuff.....
My cat, thus far, hasn't walked on any of my wares. She will however, steal my throwing sponge, the moment she knows I have it out. I have to keep it sealed in my water bucket, or she will find it and carry it throughout the house dripped clay water everywhere. In fact, just yesterday, I was getting my wheel set up. I turned my back to wedge a couple balls of clay, turned back around, and sure enough, the sponge was gone. I just followed the drip path to find it.