If "a more modern machine" includes systems with ISA, PCI or PCI Express slots, it should be easy enough to retrieve the data from the drives. You'll need a SCSI adapter (known as a host bus adapter, HBA); you can find loads on auction sites, or SCSI4ME and other places (depending on which country you live in). Adaptec cards are very good and well-supported on most operating systems. You'll also need a 50-pin cable such as these ones; avoid long cables and cables with too many connectors, you may have termination issues with your drives.
Once you've got all that, plug your adapter into your computer, connect the cable to the drive (the connectors are keyed so there shouldn't be any issue there), connect a power cable to the drive and you should be good to go.
If you can't use a PCI or PCI Express card, there are SCSI-to-USB converters, but they are usually designed for external SCSI devices so you'll need an additional SCSI converter to go from whatever SCSI port is on the SCSI-to-USB converter, to the 50-pin port on your hard drives. They also tend to be very expensive. Finally, you can also get PCMCIA SCSI HBAs for laptops, but the same issues apply, and they're even more expensive!
There are a couple of issues to keep an eye out for, but if you only connect one drive at a time they shouldn't cause any actual difficulties. The first is that SCSI drives have identifiers which can be changed, usually using jumpers; just make sure they're not set to 7 and you should be fine (7 is the SCSI HBA's identifier). The second is termination: SCSI buses need to be electrically terminated. Most HBAs from the last twenty years handle their end of things themselves, and the drives might well have built-in termination too (another jumper to look out for). As mentioned above though, if you're only connecting one drive at a time on a short enough cable, termination shouldn't be an issue.