For the Amiga and the Atari ST, I use an HXC floppy emulator, manufactured by a Polish guy. They are often on Ebay. For the C64, an Ultimate 1541, expensive, but works with just about everything, fast-loaders supported. They both use SD cards as storage. There is also a USB version of HXC, but I don't have it. The Ultimate takes MicroSD cards or USB memory sticks.
http://www.ebay.com/itm/SD-Floppy-Emulator-Rev-C-BLUE-EDITION-/170704221798?pt=UK_VintageComputing_RL&hash=item27bec3b666http://1541ultimate.net/content/index.phpIt's now possible to have direct access to the content of the SD card on either the Amiga, the Atari ST or the C64! That means you can put 2-4GB (or more) of floppy images on a card and select them from a menu on the actual vintage computer.