Push lawnmowers, dirtbikes, or chainsaws typically do not have microchips, and they are all quite complex. Also, old elevators often had purely relay logic, and I've heard that it is often more cost-effective to repair old elevators than to replace them outright, so if you live in a really old building the elevator might still be click-clacking away.

Then there are washing machines and dryers. Most new models are stuffed to the guts with computer chips, but older styles are still available, new (Speed Queen) or used (appliance refurbishment shops). Old ones are purely electro-mechanical, with some rather ingenious timer boards that do a lot with only a few contacts, a tiny motor, and a large resistor.

(I helped repair an old dryer a few months ago: the large resistor is for the dryer's auto dry mode. The wetter the clothes, the more power the heating coils will draw through the resistor, which lowers the voltage of the power the timer motor receives, slowing it down. Once the clothes start getting dry, the voltage goes back up and the timer speeds up again.)