Is there a format for a hard drive that both Mac and Windows OS can read/write to?
I want an external hard drive that stores files they can both read/write, and use for backups, etc.
FAT32 is the most supported, but its biggest flaw is that it doesn't support large files (> ~4 GiB). Next would probably be NTFS, supported (albeit not perfectly) on Mac by default (I think). Next would be HFS+, the native file system for Mac OS, but not technically supported on Windows by default. (Unless you call playing with mounting, drivers, and such "defaults").
In short, go with FAT32 if all files < 4 GB, otherwise NTFS.