This is much less interesting than the other answers. I live in a temperate rainforest in North America, in what is a fairly standard American house built in the 1950s (except for the floors being elevated off the ground, required by local building codes to reduce mold and wood rot.)

• Every spring a bunch of tree frogs invade the house and climb on the ceiling with their sticky feet and sing all night. It's cute, but once I stepped on one of them barefoot, which was quite unpleasant - worse for him than me - and now when I get up to pee at night during frog season, I use a flashlight.
• There are three pumps under the house to keep water out of it. At least one of them is running most of the time. I barely notice them now, but guests are often surprised by the rummmmmmmblesplashsplashsplash any time of day or night. We worry about getting flooded when the power goes out, which us fairly frequently.
• Growing stuff everywhere! Moss grows on our car, on the roof and outside walls, even on one of the sheep (????). Lichens grow on top of any other plant outside. A neighbor once had a mushroom grow out of a wooden chair.
• Mold is a huge problem in the house, food doesn't seem to keep very well here, even papers and books get moldy. Clothes, sometimes. Mold apparently spontaneously appears inside mattresses and furniture cushions. We have a strict schedule for when to throw away pillows and get new ones.
• Lots of noise at night - the tree frogs are about the size of a fingertip but very loud. Sometimes they crawl into the drainage pipes for the house pumps, and use that to amplify their voices into some sort of booming Darth Vader Frog thing. There are also tree-climbing foxes, who sometimes loudly fall out of trees in the middle of the night.
• We seldom see the stars, it is cloudy most of the time, and most of the native trees keep their leaves all year. Aside from a month of summer with less rain, the weather is the same all year round. When traveling, I am unsettled by a visible horizon or too much sky. It seems like any place you can see all the way to the edge of must be unbearably small.
• The trees tend to grow in lines, because new trees sprout along the fallen bodies of old ones, where the fall has cleared a gap. So sometimes you get the odd sense that the forest is organizing itself, arranging trees in specific shapes. Like being inside some enormous mossy mechanism, but not having the perspective to see what it does.