You can format a drive as FAT32, which would allow it to work on BOTH Windows and Mac, but it won't do automatic backups, won't take files larger than 4GB and will have a high risk of data corruption;
Otherwise, you can have a drive as NTFS to allow to work on any PC and then install on your Mac a free app from the Apple website called NTFS-3G, which allows your Mac to fully use (read and write) to NTFS and also do automatic backups with no restrictions on both systems, but since it is done using the NTFS-3G software, this configuration will only work on YOUR Mac and the others will only read from the drive (But they won't be able to add files).
Also, you can have the drive as HFS+ to allow you to use it on any Mac and then install on Windows a program called HFSExplorer (Free), which allows you to read (see and copy out) drives formatted for Mac (But not write, so you can't add files) or you can install MacDrive (NOT free), which is a software able to allow full HFS+ integration (Read and write) on a PC, meaning that it is the exact opposite to NTFS-3G. However the same rules apply, only PCs with this software will see drives formatted for Macs.
Note: Credits to Pizza!