Nearly all drives are compatible with both Mac and Windows. They are just usually not compatible with both at the same time.
Macs can read NTFS but not write to it, so they can read a Windows hard drive but not write to it. Windows can't read or write to HFS+, so it can't read nor write a Mac drive.
Both can read and write FAT and FAT32, but those formats don't support the large sizes of modern hard drives.
exFAT (requires OS X 10.6.5 or newer) does work, though from what I read you should format the drive as exFAT under Windows. After you've formatted the drive as exFAT, both your Windows and Mac computers (with 10.6.5 or newer) will be able to read and write to the drive.
http://lifehacker.com/5927185/use-the-exfat-file-system-and-never-format-your-external-drive-again
exFAT is optimized for flash drives, so won't be as quick on a HDD as HFS+ or NTFS, and will probably waste more space. But it's the simplest solution to what you want to do. The other options are to buy software for your Mac which will enable it to write to NTFS (Windows) disks. Tuxera and Paragon make such software, though I have used neither.
http://www.tuxera.com/products/tuxera-ntfs-for-mac/
http://www.paragon-software.com/home/ntfs-mac/