Can't believe no one has mentioned debugging...
I haven't written a line of assembly code in many years now. But I read it reasonably often. High-level debugging is great when you have the source and symbol information, but when your fancy library is throwing an unhandled exception on customer machines, it's too late to require that to be included in the license...
But I can still open up the disassembler and see what your high-level logic eventually ended up doing, trace bad data back to its origin, find out who changed the FPU control register...
This has saved my bacon more often than I care to think about. And it's never too late to learn - there are plenty of great references and tutorialsplenty of great references and tutorials out on the 'Net, and just about any program running on your machine can provide a hands-on environment.