It depends.  Some places won't let you enter if the passport is expiring in six months or less.  I had a boss that got turned away in Singapore because of this.  Everybody has their own set of rules so it pays to check it out in detail though US and Canadian citizens are very lucky since they have very lax visa rules in most countries.  I've known people that were turned down for tourist visas because they are leaving one country with a visa for that country that expires during the trip (but they are not returning to the country).  When I travelled to Europe, we had a connecting flight for the return to the States through Canada.  My girlfriend needed a transit visa even through we were not staying in Canada.  She didn't know this (previous transits through other countries did not require visas so she didn't know about such a thing), the airlines and ticket agent did not notify us, so we had to buy new tickets for a direct flight to the US on the spot.
So it all depends but it can really bite you in the ass because in the end, you have to find out about this stuff on your own.