To my surprise, the most frequently read post on The Discreet Traveler has been Top 10: How to travel with two passports. Because I keep getting questions about it--thank you, readers!--here are a few quick answers. Most questions seem to be from Americans.
The short answer is Yes, to and from the USA. The fuller answer is that you must (by law) show your US passport to US immigration officials when you enter the USA.
The law says you must enter and leave the USA with a US passport but in practice, the US does not have exit immigration like most other countries do. So the only requirement to leave the US with a US passport is that you must have the passport with you. Checking into a flight out of the US using your other passport is not a violation of the law. Airline officials are not immigration.
2. I am a citizen of X country. If I have a passport for that country, can I travel there without restrictions?
Yes, you can. It does not matter if you were born in that country or if you have never been there before. Being a citizen of a country means they have to let you in, and you never have to leave, and you have the same rights to live and work there as someone who has never left.
Now as with US citizens (1), the country may have rules about entering with its passport, and common sense says check before you travel to any country long term. But if you are a citizen of a country, it cannot refuse you entry. (A US citizen trying to enter on a foreign passport might run into fines or other problems, but s/he can't be refused entry to the US.)
3. But won't immigration officials think it's suspicious if I present a passport without any stamps in it/that's never been used before? Won't it look like I haven't gone anywhere?
This seems to be the most frequently asked, and the answer is No. First, stamps are irrelevant because many border crossings don't even stamp anymore. Electronic systems can show where you came from. If you are a citizen of a country, that country has to let you in!
4. I entered country Y with my US passport, and now I'm going to country Z. Can I use my Canadian passport instead?
Yes. You can use any passport you want anywhere in the world, except the USA. Of course, if you plan to use your other passport and need a visa, make sure to get the visa in the passport you're going to use.
Do be careful when leaving country Y if it has exit immigration (as most countries do): if you entered Y with your US passport, you need to show the same passport to Y's officials when you leave. Then, put it away and show your Canadian passport to country Z's immigration officials (and again at exit).
5. I accidentally used the wrong passport to exit/overstayed my visa/got a ban from a country the last time I visited there. Can I just use my other passport and pretend it never happened?
The short answer to this is No. You could try this, but it would be a mistake. Getting caught trying to "fool" immigration officials always has more serious consequences than just making a mistake in the first place. If you're asked a direct question, you need to give an honest answer.
Always remember that you are a person, not a passport. If you break a rule, don't try to use a different passport to get around the rule. Find out what is involved in rectifying the problem.
6. What information do I put into the Advance Passenger Information when buying a ticket online? The website only allows one passport.
At some point during the trip you will probably need to show your other passport (for example, at exit immigration from the country you're flying from). Just show the immigration officials the passport they need to see. It does not matter if it's not the same one you used to check in.
7. I'm still confused. Isn't it better just to show everything to every official and let them pick what they need?
Not really. They tend to be to-the-point people and don't want unnecessary information--which is why you should keep your answers short.
Having said that, if you're asked something that can only be answered by your other passport, just tell them. It is not illegal or as uncommon as people seem to believe.
Travel safely. Have a great time. Don't worry; be happy!