Yep, the biggest problem with reading data from the old floppies is that the disks themselves seem to develop unreadable sectors after sitting in one place for 10 or 15 years or more. I think the magnetic particles start to align North-South or something, instead of the way that gives the data some meaning.
I recently removed the last floppy drive from any of my computers. I had considered doing that a year ago, but I *knew* that as soon as I did that, someone would show up with a floppy disk and ask me if I could copy the contents to a flash drive for them. So I held off. No one asked...
I finally removed the floppy drive last month, and sure enough, two days later a friend asked me to copy some data. I knew it would happen!