Used to get birds in my parents house, jackdaws would fall done the chimney and land the kitchen, would shut the cats in another room, open the window did and herd it out with a broom. One got stuck behind a wardrobe once, i thought we had a poltergeist, i was home alone and the wardrobe was too heavy for me to move, i had to call my ex to come and help me.
We had mice in my old flat, lots of spiders; big ones. Had an infestation of flying ants once, it was horrible.
Had smaller spiders in the house, no rodents thankfully. Next doors cats have visited a few times, I'm pretty sure one wants to move in with us but our cat wouldn't like it. He is always in our garden and makes a beeline for the door if it is open, have had to put a zip up mesh on the back door to keep our cat in and him out.