Fallen trees aren't just useful for furniture and firewood. You can use the wood to form the backbone of a type of gardening known as Hugelkultur, which involves burying wood in your garden bed.
Permaculture site Rich Soil promotes the many benefits of Hugelkultur:
Hugelkultur is nothing more than making raised garden beds filled with rotten wood. This makes for raised garden beds loaded with organic material, nutrients, air pockets for the roots of what you plant, etc. As the years pass, the deep soil of your raised garden bed becomes incredibly rich and loaded with soil life. As the wood shrinks, it makes more tiny air pockets - so your hugelkultur becomes sort of self-tilling. The first few years, the composting process will slightly warm your soil giving you a slightly longer growing season. The woody matter helps to keep nutrient excess from passing into the ground water - and then refeeding that to your garden plants later. Plus, by holding SO much water, hugelkultur could be part of a system for growing garden crops in the desert with no irrigation.
You can use freshly-cut wood as well as rotten wood, but keep in mind that newer wood will consume nitrogen as it composts, which could bother some plants. As the wood decomposes it will leach the nitrogen back into the soil, so you will actually see a gain in nitrogen over time, but in the first few years you may have to add supplemental nitrogen for some plant types.
If you're interested in learning more about Hugelkultur the source link below has multiple videos, lots of photos, and a much more detailed section on how the beds work.