Maybe. Some countries require the passport to be valid for a certain period of time past the travel date.
Often, the requirement is for six month of validity still on the passport after the trip is over. That means, if your passport is going to expire just a couple weeks or a couple of months after you get back, you may not be permitted on the flight, the country may detain you upon entry, or they could deny your visa request. The Department of State's Country Specific Information is useful for determining such details, or check with the country's consulate, if you already have that contact information.
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