Does SCSI count? I had this thing called a Zip Drive that took Zip Discs. It was practical for about 6 months.
Scuzzy is a parallel interface. External Zip drives came in both Parallel Printer Port and SCSI interface variants.
Keep in mind that, in the 80's, serial was very, very slow; the first UARTs (original 8250) combined with an XT class machine could barely work up to 4800bps due to the amount of interrupts it generated, while the 16450 (on a PC/AT class machine) could only reliably do 9600bps (maybe 14.4Kbps+ if you used a protocol with error detection like Kermit or Zmodem).
In the early 90's, the 16550 was released, which had a 16 byte FIFO and could generate interrupts at 1, 4, 8 or 14 byte intervals. Unfortunately the original 16550 had an issue where the FIFO didn't work; this was corrected in the 16550AF silicon, circa 1992.
The 16550 is pin *and* software compatible with the 8250/16450, meaning you can replace the factory UART in old XT/AT class machines. The 16550's registers will look like an 8250 until a command is given, then it will go into 16550 mode; this way it even works with old software.
Using a 16550, you could reliably do 115.2Kbps over serial. Some ISA Serial Port cards with 16550 (and '650, '750, '850, etc.) UARTs allow you to set a clock multiplier, so you can even reliably do up to 460.8Kbps! (Which is nearly as fast as a vintage 5.25" floppy drive.)
In fact, the XTIDE Universal Bios (which is a bios extension that allows you to run large hard drives / flash storage on vintage machines) has a feature that allows you to boot from a virtual floppy or hard drive over serial. You run the server software on a Windows/Linux/OS X machine, select the imagine and boot the target, when XTIDE loads you hit a key and it try's to access the image via the serial port. It's very useable for loading a fresh copy of DOS on a new machine, even at 115.2Kbps! (Though it would be a bear at 9600bps...)
Anyway, my point is that for a 1980's class machine, without a 16550 UART, using the serial port for storage is going to be painfully, painfully slow. It's doable, but even an original non-EPP Parallel Port would be better (which is 8-bits write, 4-bits read).