Jeanne Kramer-Smyth, the author of Spellbound Blog, has written a piece on transferring data from old 5.25" floppy disks. This follows Jason Scott's July 12 post where he offers to help people retrieve data from these old disks. He also wrote a procedure for how to do it. Scott said that a growing number of organizations and people are focusing on this, but that they are focusing on it too late. The data on those disks may already be gone. However, if you have 5.25 floppies, check out the Kramer-Smyth and Scott blog posts for information on how to rescue that old data.
If you have 3.5" floppy disks, you should be considering what to do with them now. There are still 3.5" disk drives around, so you do have the possibility of reading those disks and transferring that data from them, without a huge amount of hassle. Now would also be a good time to decide if you just want to toss the disks in the trash and forget about them. If you are going to throw away any disks, remember to render them unreadable by harming the media, especially if you think the disk contains any sensitive or confidential information.