This is a problem that comes up in the DMS from time to time. Patrons come in and say, "I've been using this external hard drive on a mac for a long time and suddenly it won't work; I can't put files on it." My first question is always the same: "Did you use it on a PC?" They usually shrug and look at the floor, "yes."
This is a problem and it can create some misleading assumptions. Flash drives (thumb drives) can move fairly effortlessly between Mac and PC since they are basically solid-state memory. External hard drives, on the other hand, are an entity unto themselves. As such, they live by different rules.
When a Mac-formatted external hard drive is plugged into a PC, the Windows OS can sometimes attempt to appropriate the drive's file system for its own. Then, when the hard drive is plugged back into a Mac the Mac is unable to write to the disk. There are two solutions to this problem:
1) Prevention - DON'T use your Mac external hard drive on a PC. Just don't. There's a very low chance that your disk will become unwritable if you do this.
2) Cure - If it comes to the point where your Mac-formatted hard drive has become unwritable on a Mac your only option is to reformat the drive. Some folks will tell you that you can "repair the permissions," but this is almost never possible. BEFORE you do this make sure you backup all your data; once you tell a Mac to reformat there's NO WAY to recover any data left on the drive. Here's a video tutorial on how to format an external hard drive on a Mac.
One option you have, if you insist on your drive being useable on both systems, is to partition the drive with some percentage reserved for Mac and some percentage reserved for PC. Here's a video tutorial on how to partition a drive.
If you decide to take this route, make sure that you set the formats as follows:
Mac partition - Mac OS Journaled (extended)
PC partition - NTFS
DO NOT USE Fat32 for any reason. This file system was intended to be a cross-platform solution. Unfortunately it will not allow the transfer of files larger than 4Gb. If you're doing video work or some other heavy multimedia lifting Fat32 will only complicate your life.