But back to the OP, could I just go to my local International Airport, hop on a flight to North Korea with passport in hand and be admitted into NK?
I don’t think you can just buy a plane ticket and show up in North Korea; I’m pretty sure you have to book a “tour”, where of course you are assigned minders who make sure you only see what their government wants you to see. I’m pretty sure there are American journalists who have traveled there as well, I don’t know if they had to do a tour per se, but I’m sure they were assigned minders as well.
The one country where Americans technically aren’t allowed to travel is Cuba, except for a few approved reasons. Until a few years ago it was not possible to buy a plane ticket between the US and Cuba, but an easy way around that was to fly to Mexico, and then buy a separate ticket from Mexico to Cuba. But recent administrations have interpreted the “education” exception so broadly that nowadays Americans effectively can just travel to Cuba.
I have had to get visas ahead of time for China and India (which cost); whereas Tanzania, Turkey, Jordan, Egypt we got a visa on arrival - also usually with a price.
I don’t recall any such requirements for Europe, Dubai (UAE), Australia or New Zealand, Hong Kong (about 10 years ago). I understand a lot has changed in 10 years, thanks to the ubiquity of online processes…
Note that China required us to mail our passports to their embassy; India needed a photocopy of the main page of the passports, both for simple tourism visas. Even applying online, India took a day or two. (Print out the approval email and have a copy available at Indian customs) So for OP, you couldn’t just hop on a plane tonight and be there. These took a while.
The fee for Turkey (and I understand, for Brazil when we were looking to go there) was a tit-for-tat reaction to Canada and the USA charging fees and needing visa applications from those countries. In most cases where you pay for a visa on arrival, the process is usually quite fast - fill in a form, maybe, present passport, pay money. Often, they require cash - preferably American dollars - not credit.
From some travel show I saw ( “Departures” ) it appears that a North Korean visa application is processed through certain approved travel agencies in China, so you then fly in from Beijing, and get assigned a tour guide who shadows you all the way.
Cuba is a popular Canadian tourism destination. I know a number of people who have been there.
As I read the OP, they were wondering about flying your own private jet there. As I gather, international flights (obviously) must land at an airport with customs control. Plus, you must file a flight plan with air traffic control before you leave. Not sure what the issues are about getting landing approval but obviously having your own jet does not exempt you from the standard visa requirements.
No, but there are lots of countries where that is true.
Not arguing that. But the OP was curious if that is true for every country with flights from the US.
You can’t fly to lots of countries without a valid visa. The airline won’t even let you board until they’ve checked that you have all the paperwork needed to enter because if not, they’re on the hook for sending you home. As mentioned in this thread, you can’t fly to China without a visa. I’ve had to get visa for a few places before leaving the US, although some (like India) now allow you to get a tourist one at arrivals. I’m pretty sure I needed a visa for Nepal before leaving the US.
I don’t know how “funny” I actually find that. Sounds like you were put into a rigamarole and a potentially bad situation because the airline screwed up. Yikes! Glad it worked out for you in the end.
To the OP I always register my foreign travel plans with the State Department regardless if it requires a visa or not. Never know if the political landscape goes south and they need to send the Marines for you. 
Also, Turkish Airlines has a huge hub at Istanbul. They fly to Tel Aviv several times a day. It’s a very popular way for Israelis to travel; one can fly to pretty much any major city in the world via IST.
St Helena only got an airport recently. Pitcairn island does not have one.
Delaware (the state) did not have a commercial airport during some periods. Everyone would go to Philly or other airports. Now they only have 1 fight to Orlando.
Well dolphinboy or whoever made his travel arrangements screwed up. The airline didn’t catch the error, which is a screw up as well. But if they caught it he would have been turned around from the starting point, he still wouldn’t have made it into Brazil.
Checking to see if a visa is required for international travel is first and foremost the responsibility of the traveler.
It seems, like several other European airports, that if you transit through Istanbul and are not leaving the zone behind customs, you don’t need to worry about a visa. The only boring part we had was waiting 5 hours in a not very interesting area to get to Addis Ababa - which also had a no-visa area for transiting passengers.
The simplest way to get from Cairo to Jerusalem for us was via Istanbul, so we stopped over there for a few days. Then, we had to buy a visa, which IIRC was about $60US each - again, a tit-for-tat over what the Canadian government did to Turkish visitors.
We flew a budget airline from the secondary airport - let’s switch continents for the next flight. (Gokcen airport) The flight was remarkably cheap on Pegasus airlines, but the seats were extremely narrow and cramped for us overweight North Americans, and we arrived in Ben Gurion close to midnight. (When we got dropped off near our hotel in Jerusalem, the bar across the street was very rowdy, the crowd loudly singing along to “Always Look on the Bright Side of Life”)
That there is even a budget airline flying there suggests some pretty good traffic. Remember until recently, Turkey was an outlier in being relatively friendly to Israel unlike the Arab countries.
The visa entry requirement for Turkey seems really random - you don’t need one from the UK, but you do from Ireland. You don’t need one from Denmark, but you do from Belgium, etc. Tit for tat indeed!
Hong Kong (and Macao) are still visa free for many Western countries; as far as immigration is concerned they operate independently from Mainland China.
This is not entirely accurate for everyone - you need to get your visa from the country that is your main destination (based on longest stay and purpose of visit) unless this is hard to ascertain, in which case it defaults to first country of the multiple main destinations. So if you’re flying to Netherlands, are there for 1 day, then 5 in France, 2 in Finland, and 5 in Switzerland, you need to apply to the French embassy.
Of course, US citizens don’t need a visa at all, for short visits to the Schengen zone (but will need some other documentation like proof of finances - I believe a credit card will do).
Concerning the visa policies that apply to US citizens, Wikipedia has a map:
The map is an oversimplification, of course — there are probably all sorts of secondary rules for each country — but that should give you a sense of how likely you are to need a visa and to which countries you can just “show up”.
As far as the detail of which countries don’t have an airport to fly to in the first place, it appears there are five, all of them European microstates: Andorra, San Marino, Monaco, Vatican City, and Liechtenstein.
As an aside, there are also short-term “transit visas” when you are passing through another country. It could just be one for the airport, or it could be a multi-day one allowing you to travel on your way to another country (for example, some friends of mine got a 3-day transit visa for Iran when driving from Turkey to Pakistan. This meant a lot of concentrated driving, as 3 days is not a lot to get across a big country like Iran. Driving non-stop, it’d be about a day and a half.)
I"ve dealt with a good number of visas, and it can get pretty goofy. With Moscow, we didn’t stay at a hotel and we didn’t want to reveal our travel plans (we went as journalists cough I mean tourists), so we had to pay a company something like a hundred or hundred fifty bucks to get an expedited visa where we were nominally employees of a Russian company. So this “company” was doing the inviting, and we had to give no further information. We did this two times, and got our visas nice and quick. The first time we just went the regular friend-inviting-us route, but it took much too long and was a frustrating process at the time (c. 2000). The “business visa” route went completely smoothly, no hassles at the border coming in or out, nothing. No questions about our “employment” with the company. No need for a backstory. It’s like everyone knew what was up and let us through.)
My father went to Australia about 30 years ago and didn’t realize a visa was required. He was able to get a visa on arrival at the airport but it was not a fast process.
Nowadays, depending on what passport you hold, you can get an electronic travel authority for short visits to Australia online in a few minutes. But you would still be advised to do it before you go to the airport.
That can’t be right? Until Freddie Laker came along, my dad said he made a point of flying Icelandic Airlines to Liechtenstein (? I think) because they were outside the cartel of transatlatic airlines that charged outrageous prices.
I think you mean Luxembourg (IATA airport code LUX).
They’re both small territories, but Liechtenstein is really tiny, and tucked up into a mountain valley. I don’t think they’ve ever had so much as an airstrip, much less an international airport.