What format for my external drive allows use with Mac and Windows? How can I use my external hard drive on Mac OS so I can modify/edit files on both OS's: Mac and Windows? How should I format it?
FAT32 (called MS-DOS (FAT) by Disk Utility; a filesystem originally released in 1977 and updated a few times since, lastly in 1996) really is the only cross platform filesystem that is going to work fully out of the box with Windows and Mac OS X.

Be careful though, if you are using Disk Utility to format the drive, you should make sure to choose the Master Boot Record partitioning scheme (hit the "Options..." button below the "Partition Layout" control on the Partition pane). The default GUID partitioning scheme won't be recognised by 32-bit Windows XP and earlier Windows operating systems and Mac OS X versions earlier than 10.4.

Mac OS X has had support for reading NTFS formatted disk for a few versions, but still doesn't have write support. There are a few third-party products that allow Mac OS X to read NTFS formatted drives but as far as I'm aware the free ones aren't as well maintained as the commercial ones. I'd love for someone to tell me differently. For a while I've been using http://code.google.com/p/macfuse/ but as far as I can tell it hasn't been updated since December 2008.

Tuxera (who develop one of the commercial NTFS drivers for Mac OS X) have a list of free NTFS drivers that are developed from the same NTFS-3G source used by Linux to read NTFS drives. http://www.tuxera.com/community/ntfs-3g-download/