By far the most common I see/write are long switch statements or if/else semi-switch statements for types that can't be used in this language's switch statements (already mentioned a few times). Generated code is an interesting case, but I'm focusing on human-written code here. Looking at my current project, the only truly long function not included above (296 LOC/650 LOT) is some Cowboy Code I'm using as an early evaluation the output of a code generator I plan to use in the future. I'll definitely be refactoring it, which removes it from this list.
Many years ago, I was working on some scientific computing software that had a long function in it. The method used a large number of local variables and refactoring the method kept resulting in a measurable difference per profiling. Even a 1% improvement in this section of code saved hours of computation time, so the function stayed long. I've learned a great deal since then, so I can't speak to how I'd handle the situation today.
