We do, quite a bit. I print out documentation for my programming work because sometimes I want it sitting on the desk next to me so I can scribble on it, maybe highlight some lines, write little checkmarks, etc., rather than having yet another pdf window open. My wife sells stuff online so she prints shipping labels and patterns. When I find a recipe for dinner I print it out and clip it to the side of the fridge so it's next to me while I'm cooking (I don't want a tablet or laptop in the kitchen that I then have to scroll up & down with greasy fingers). If it's a recipe I think I'll do again, I save that printout in a plastic sleeve in a big binder. I know I could just save the bookmark, but web sites tend to disappear or go behind a paywall surprisingly often, and again, I can scribble notes on the printed recipe that I can't on a web site)
Contracts, legal documents, etc., I save them as PDFs on my file server but I also keep printed copies in a file cabinet as backup.
And yes, we own a Brother printer because they have been the most reliable and trustworthy for their price.