With few exceptions, leaving the United States while a green card case is pending can be fatal to one's case. In general, departure from the United States without an advance parole document normally results in a denial of the adjustment of status petition. USCIS will determine that the individual has abandoned the application. Moreover, in some cases, if an applicant has overstayed and accrued too much "unlawful presence," he or she may trigger a three or ten-year bar from returning (depending on the length of the unlawful presence). So, in most cases, if an individual foresees that he/she will need to travel outside the US during the pendency of an adjustment of status case, advance parole should be strongly considered.
If you are a permanent resident planning on traveling abroad for an extended period of time, it may be worthwhile to explore your options with an immigration attorney. Green card holders must be cognizant of the abandonment of permanent residence issue, which potentially comes into play anytime a permanent resident spends more time outside the US than inside. Abandonment of a green card may also be implicated when a resident travels outside for more than six months, and especially so if the permanent resident stays outside for one year or more.