Not quite a getting stuck story, but pretty close. Back about 1966 the Corp of Engineers began filling a federal resevoir near my hometown. My grandfather and uncle farmed some of the ground which was going to be covered when the dam was full, which was expected to take about 2 years. They had wheat almost ready to harvest that year when unexpectedly heavy spring rains soon had the water backing up into one of their wheat fields.
Trying to salvage what they could of the wheat crop, they reversed the front drive tires on the combine and would then cut into the mud from the rising water until the wheels began to spin. Then they could simply back out of the mud because the tire lugs would be in the right direction for best traction.
They did manage to get some wheat out of what would otherwise have been a total loss. It was really fascinating to watch. From behind, it almost looked like they were cutting into the lake as the water rose into the far end of the field. Some of our neighbors had fields that filled in as short as two hours.
This is probably old hat in other areas that getting flooded frequently, but it was the first and only time I've seen anything like it. I think about my grandpa and my uncle nearly everytime I hit some serious mud with my combine!
GGB