We have electrochemistry kit that is chugging along on a PC running Dos 6.2 and Win 3.11.
Getting your data off requires a floppy disk as an intermediate step. I have no idea what we'll do if that machine ever craps out - it would be a shame to have to retire the potentiostat because the computers that it was designed to talk to have effectively ascended to godhood in the meantime.
It's certainly not the only piece of analytical kit that is tied to legacy hardware. We have a couple of FTIR machines that look like props from Fallout: New Vegas but work just fine and I'm pretty sure the EPR computer is running Win95.
I shudder at the thought of using a floppy. I like the software FastLynx Kind of like Interlink, but it can easily drag and drop files from DOS to a Win95/98/ME/NT4/2K/XP/Vista/7/8 (32 or 64 bit) using Serial or parallel null modem cables. Cheap $2 USB-serial adapter can be had on eBay. To get faster Parallel transfers requires a real LPT port on your modern PC, not a USB adapter. You can get the bundle from them that includes the software, and cables.
If you have a PC with a broken floppy drive, it can even send the software using MODE and CTTY commands.
It also comes for licenses of Windows versions of Interlnk and Intersvr. The way I had it set up, I created an up to 2GB FAT16 Truecrypt image on my modern "Server" PC (you can use some other image software as well). This gets mapped to a drive on the legacy client machine so now you have a massive disk drive expansion. When the drive is mapped, FastLynx has exclusive use of it, and you can't access files on the host OS it until you disconnect from the legacy PC. Alternatively you can map the drives on the DOS PC onto your modern PC.