How Can I Safely Dispose Of My Old Floppy Disks (with Personal Data)? I Have Over A Hundred Them And No Longer Need Them.

If the data is "that personal ", then destroy them. Get a metal garbage can, some wood, a little gas to keep the wood burning. Chuck them in.
DON'T BREATH IN THE SMOKE & VAPORS..." DANGER..Will Robinson......DANGER....Will robinson"
2nd-LLpn ="donate them" is a very good idea. Floppy are expensive for someone of little means. PS you would STILL want to erase the personal data!!
3rd. Radio Shack or another electronics shop sells a "Deguissing Coil", nothing more then a large coil of wire with a resistor in series that when pluged in sends out a heavy magnetic field that will erase the floppies when placed in the field of the coil( inside the loop).
4th-Ask someone you know & trust with a computer & floppy to format them before giving away or disposing of them.

I would call a shop that does repairs to computers, and see what they say about it. For all you know they might want them for parts or whatever. Hope this helps, good luck.