Originally Posted by USCIS
International Travel
A Permanent Resident of the United States can travel freely outside of the US. A passport from the country of citizenship is normally all that is needed. To reenter the US a Permanent Resident normally needs to present the green card (Permanent Resident Card, Form I-551) for readmission. A reentry permit is needed for reentry for trips greater than one year but less than two years in duration.
You can find more information about travel documents from "How Do I Get a Travel Document?"
Maintaining Permanent Residence
Maintaining Permanent Residence You may lose your permanent residence status if you commit an act that makes you removable from the United States under the law in section 237 of the Immigration and Nationality Act. If you commit such an act, you may be brought before the immigration courts to determine your right to remain a Permanent Resident.
You may be found to have abandoned your permanent resident status if you:
Move to another country intending to live there permanently.
Remain outside of the US for more than one year without obtaining a reentry permit or returning resident visa. However in determining whether your status has been abandoned any length of absence from the US may be considered, even if it is less than one year.
Remain outside of the US for more than two years after issuance of a reentry permit without obtaining a returning resident visa. However in determining whether your status has been abandoned any length of absence from the US may be considered, even if it is less than one year.
Fail to file income tax returns while living outside of the US for any period.
Declare yourself a “nonimmigrant” on your tax returns.