Years ago, in one of the first places DH and I rented together, we had a wood burning stove. I woke up one morning and heard this noise inside the stove. I was a little freaked out, but determined to be brave so I carefully opened the stove. Out flew a bird! It had gotten down the chimney flue and got stuck in the stove. It was in there hopping around among the ash (thank goodness we were going through a warm spell and hadn't had the stove on for a few days). It freaked me out to see that bird fly right at my head though. I woke up DH and he got it out of the house for me.
Years later we lived in a house that was a huge money pit and big construction problem. The back half of the house didn't have ceilings at all (or walls, or flooring, just plywood on the floors. The front (finished) part of the house had a small attic. Apparently we had squirrels in the attic and they discovered they could come through to the unfinished part of the house and roam around. We were always finding something back there. We went on a trip and came home to find several dead squirrels in the house. The cats apparently decided they made good play things. We also had several birds get inside that house.
The last house we rented had a mice issue. Oh my gosh! It was awful. They just appeared suddenly one day and we could hear them scratching in the walls and between the upstairs and downstairs. One day the cat was acting funny so I tracked her down and there she sat with a mouse in her mouth. She let it go when she saw me and it took off like lightening. Then the chase was on to see who would catch it first, the cat or me. The cat won. I finally ushered her with her 'prize' in her mouth outdoors. Over the next two weeks or so, we caught probably 20 mice. Some of them were teeny tiny babies. Those I would just turn a can upside down over and scoop them up. I took them and let them loose outside (far from the house). There was no need to kill them, I just didn't want them in the house. We did find several dead ones though too.
This house we've had a couple of visitors. We have moles in the yard, or did when we first moved in, I haven't noticed any lately. We kept waking up to dead moles on our front porch. It freaked me out because before I realized they were moles, I had no idea WHAT they were. We found a dead mouse by our hot water heater which is in the kitchen. That was kind of odd. Then one night we're sitting here an I see something scurry by. DH looks up at me and said "was that what I think?". I told him I thought so. He started moving stuff and there was this big furry mouse. It looked like someone's pet mouse from a pet store. It was obviously well fed, had soft, fluffy hair and wasn't afraid of us at all. DH caught it (it basically crawled up in his hand!) and took it outside and let it loose in the woods across the street from our house. We haven't seen another and not sure how that one got in here, but it shocked us as it really seemed like a pet or something. None the less, without knowing for sure, it isn't living here!