For US citizens, are there any locations outside the 50 US states that don't require a passport to fly to and from?
You can re-enter the US if you have proof of citizenship, so that doesn't strictly require a passport -- although it may make your enter procedure more troublesome.
As mentioned above, you can theoretically travel to US territories without a passport, from answers.usa.gov:
For Travel to/from/between U.S. Territories, U.S. Citizens and Nationals:
You need a photo identification or travel document when visiting American Samoa, the Commonwealth of the Northern Mariana Islands (CNMI), Guam, Puerto Rico, or the U.S. Virgin Islands. Your itinerary and/or carrier may require this document to be your passport. You also need proof of citizenship and either a return or onward ticket, or proof of employment in the territory, to visit American Samoa.
Also from that page:
For Travel to/from/between Freely Associated States, U.S. Citizens and Nationals:
You may need a valid U.S. passport, birth certificate, or naturalization papers to enter a Freely Associated State.
If I'm right that covers Palau, Federated States of Micronesia and the Republic of the Marshall Islands.
However, from visit-palau.com:
All visitors must have a valid passport not less than 6 months from date of expiration and proof of return arrangements. [ ... ] Citizens of United States of America, Federated States of Micronesia, Republic of the Marshall Islands, Guam, and the Common Wealth of Northern Marianas Islands with valid passports are issued 1 year Visa upon arrival.
so that's out but from visit-micronesia.fm:
U.S. citizens may enter any FSM state with a U.S. passport or proof of U.S. citizenship (birth certificate). Non U.S. citizens must have a valid passport from their country of origin.
So there's another option. I can't find an official page for the Marshall Islands but passportsandvisas.com says you need a passport.
It appears you used to not require a passport for Mexico or Canada but this changed in 2009/2010 and now everyone requires a passport to cross those borders.
Also note, if you're flying, airlines may very well insist on a passport or at least make your life difficult if you don't have one. But technically passport-less travel is possible to the places mentioned above.
I'm not sure how things like privately owned islands work -- could you theoretically fly there without a passport? I'd also imagine you might be able to persuade a cruise company to let you helicopter out to their cruise liner and land on that, which might count.
US, Canadian, and Mexican citizens can fly between the US and Canada on their NEXUS card. http://www.nexus.gc.ca/prog/nexus/menu-eng.html
US and Canadian citizens can use a NEXUS card to fly between the US and Canada.
In addition, a few Caribbean countries (such as St Lucia and - for Canadians - Bonaire/St Eustatius/Saba) let these nationals in (yes, by air as well) with a birth certificate and photo ID, or a certificate of citizenship/Canadian citizenship card.
Canada also lets US citizens in (flying from anywhere) with a US birth/citizenship/naturalization certificate.
However, for a US citizen to re-enter the US by air, a passport or (coming from Canada) NEXUS card is needed. Same goes for Canadians re-entering Canada by air other than from the US