I'll need to research this some more, but I'm going to guess that the following is not totally inacurrate:
- Master Boot Record (MBR)- the most common, this is highly compatible, and can be used for making a Live USB, among other things. Most hard disks are formatted like this.
- GUID Partition Table (GPT)- is used for very large (more than 2TB) hard drives. It is newer than MBR and the two are not compatible. This may not be the right choice for 1TB external hard drive. See http://en.wikipedia.org/wiki/GUID_Partition_Table.
- Don't partition - the rough equivalent of rubbing a magnet on the side of a drive, but with a much lower risk of damaging the drive. Not recognized in Windows. Can't use NTFS.
- Apple Partition Map (APM) - Is a legacy format introduced with the 680x0-based Macintosh II in 1987. The format was also used in PowerPC Macs. Apple switched to GPT with Intel's Extensible Firmware Interface (EFI) in 2006 for Intel-based Macs. see Apple Technical Note TN2166 "The Road to GPT" section for more details.
If anybody knows about the GUID Partition Table, or knows what the purpose to the Apple Partition Table is, feel free to edit it in to my answer. ;)