Right-click the drive (in Windows or Mac OS X), and see what filesystem it's using.
If it's using NTFS, then there's the problem.
NTFS is Microsoft's proprietary filesystem that they use with XP, Vista, etc. They don't give out the instructions to write to it to other manufacturers, like Apple. Hence why you can't write to it on a Mac.
A better filesystem to use for total compatibility is FAT32. Only issue is that each individual file can be no larger than 4GB in size. But this may not be an issue for you.
This can be changed in disk utility on a Mac, or by formatting under Windows. Note that if you do this, copy your data somewhere else first, because you'll lose it.