When is the GUID partition table (GPT) preferred over Apple partition map (APM) for external drives? I have seagate external portable hard-drive 1 TB, and I will be using with following Mac's.

13" White MacBook (Intel Core 2 Duo) running Snow Leopard
13" MacBook Air (Intel Core i5) running Lion
iMac running Lion

What partition map I should use, GUID or Apple when formatting external portable hard-drive?
It's always better unless you must use the drive with an OS that is too old or too different to support the GPT format. Windows, Unix, macOS all support GPT / GUID and APM is not widely supported on other OS.

To elaborate, GUID (or more properly GPT - the GUID partition table scheme) is the new bootable standard for Macs so use it unless you have macs that need to boot from this drive and cannot support GUID. APM is your only option in that unlikely case. The vast majority of macs will work with both in all instances - especially if you don't need it to be bootable.