OK, so we all know that travelling is not just ticking off countries but I'm sure many members here are often asked, "So how many countries have you visited then?". What do you count as having visited a country (or a region or a place)? If you have to change planes at Riyadh, can you count that as a visit to Saudi Arabia? What about an afternoon wandering around the streets of Monte Carlo; can you tick the Monaco box? A couple of hours in Vaduz for Liechtenstein? How about a delayed plane after a refuelling stop at Nairobi which results in a stay in a city centre hotel overnight for Kenya? Getting off a ferry at Zeebrugge and being herded onto a coach bound for Germany; can you tick off Belgium? A plane change at Singapore with enough time to do the airport's bus tour of Singapore City?
What counts as a visit?
I only have one of these difficult ones - six transits through Doha airport. Since I now answer vaguely "over a hundred countries" it doesn't make a difference.
This stuff should only matter to extreme tickers. And they should get over it and start travelling instead!
To answer the question, if I'm totalling up I count any visit. If I've put feet on the ground then I've been there, and I suppose if I'd cruised past looking at the scenery without putting feet on the ground then I've also been there.
To me, the question applies to the whole continent of Asia. I have changed planes at Kuala Lumpur four times. So, have I been to Asia? Somehow, but not reall y...
I think for me it's about intent. Did I purposefully travel to a location (on any scale) in order to see it? Or was I just there for changing planes, attending a business meeting (without any free time before or after), and could that have been anywhere else without affecting my plans at all?
I find the determinations easier when I just think about it on a city level. (I've changed planes in Panama City; I haven't visited Panama City.) Countries are weird anyway. Yes, I've been to Dublin for four days (so truly visited it), but no, I haven't seen anything of (the rest of) Ireland, so I don't generally count it. For me, to visit a country, I need to really go there to see the country; that means at the very least traveling around through it.
That's my internal mental determination, though. I don't care one whit if other people use less strict criteria. And hey, if anyone purposefully picks a flight so they can change planes in [new location] in order to tick it off, then that fulfills the intent criterium, so good on them. 
[ Edit: Edited on 11-Mar-2018, at 00:56 by Sander ]
If you never left the airport I don't think you can count it as visited a city or country. Personally I don't feel I can say I visited a country if I have only seen one city. I spent a whole day in Helsinki due to a flight connection, I took the complimentary shuttle, I crammed the main sights in, had some yummy food, got a little lost but that was fun
However if anyone asks I would never say I visited Finland. I feel I have to have visited at least one whole region of a country before I can say I travelled that country, and with micro nations I would say one city pretty much counts as a whole region so I am good to say I have travelled through Monaco
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I certainly don't count changing planes as visiting a country, but if I have left the airport and wandered around the country a bit I would count it. Places I have technically been to but would not count are Ethiopia as I only changed planes twice and India as I only landed, waited for passengers and left.
I count Monaco which I spent a day wandering, but did not stay overnight and Slovakia where I spent a day wandering Bratislava.
Some countries are small - So I think almost anything in a small country would count as a visit. One stop i Bonaire by a cruise ship, counts as a visit. A morning in the Vatican counts as a visit. But two days in St. Petersburg Russia does not count as having visited Russia as there are vast areas of Russia to be visited outside of the region around St. Pete.
On the other hand, you can't really visit a city in a country without also visiting the country and that's how most people visit a place.
Also there is a more restrictive criteria to use - more than a visit. Can you say that you know the country? I am familiar with my home country (even though there are three states out of the 50 that I have not 'visited') I have done quite a lot of traveling there over some period of time. So multiple trips/visits or visits to multiple places and you could say that you know the country. And that's better than just a visit.
Even though I am quite familiar with my country, I am not able to give advice on some cities - like New York City. I have been there several times, but I haven't been a tourist in NYC for quite some time. I can't tell anyone about restaurants or nightclubs (actually there are very few places where I can give advice about night clubs) or how to get tickets to the tourist destinations in NYC because I really have not visited there in 10 years and that visit was just to go to Ellis Island. Before that the last time I touristed in NYC was 1971. So I don't really know NYC the way I know Baltimore (where I grew up).
[ Edit: Edited on 11-Mar-2018, at 10:02 by greatgrandmaR ]
The bottom line for me is that you have to at least left the airport! So I've changed planes in Bogota but don't claim to have visited that city, let alone Columbia! Likewise Abu Dhabi (though I'll be seeing more of that one in a week or so as I have a business trip there) and Johannesburg. But I'll claim Liechtenstein on the back of an afternoon in Vaduz earlier this year, Monaco after going to a football match there, and the Vatican after one day. I'll certainly claim Russia after a week split between Moscow and St Petersburg, plus the train ride between the two 
Basically, if I've spent time there and seen at least a few sights, I'll say I've been to that country. What I won't claim is to know it, which in my mind are two very different claims 
[ Edit: Edited on 11-Mar-2018, at 09:59 by ToonSarah ]
Thank you all!
I agree that a visit to just one city in a large country doesn't mean you know or are familiar with the country as such, even through you might be somewhat familiar with that city.
I always used to accept that you had to sleep in that country to have it 'count' and it always bothered me that Belgium came up on my Travellerspoint list after I'd logged the visit to Germany ('ve since walked around and slept in Brussels). But visiting although not sleeping in Monaco, Liechtenstein and the Vatican has changed my opinion and I personally feel I can count these three.
The forced sleep in Nairobi fulfils the 'sleep in the country' criterion but I went from airport to bus to hotel to bus to airport and saw practically nothing of Kenya nor Nairobi - that one does bother me a little. The Singapore one doesn't apply to me but that one is a grey area.
Saudi Arabia will appear on my TP list of countries soon because we have an airplane change there next month but, as ToonSarah says, not leaving the airport isn't much of a visit - it'll bother me until I can arrange a proper trip to Saudi. And I think I'll have a sightseeing day but not a sleep in Helsinki in July too, accompanied by a passport stamp - does that count?
This is a good question. I have been asked the "How Many Countries?" question a lot. Here, it seems I have a pretty average travel history, anywhere else I am considered well-travelled.
I've decided, for myself, that I can say I've been to a country only if I have spent two days, and one night there. I've been through Reykjavik a few times, and once had to sleep for a few hours, but I refuse to count it as my having been to Iceland. I think flying into an airport, no matter how many times, doesn't count. The Airport is it's own entity and doesn't much reflect it's location (with the exception of airport trinkets) I trained through Belgium several times, and counted that for a while, but then I had to make it legit and visit the place on purpose. I went to Andorra and slept over only so I could say I've been there. That was spurious, but Andorra is very very small.
On the other hand, I count the Vatican, because if they can count the place as a country, then so can I. Liechtenstein is so small that you can count it, by just having been there. I've never been to San Marino, but I think one could have counted spending a day there as having counted. On the other hand, I once spent a couple of weeks in a border town called Tabatinga in Brazil At the very western edge of the country. Did I really see the country, though? I have since travelled a big chunk of Brazil, so the question, for me, is now an intellectual one. But I don't think it's fair to say I visited the country in a real way before that second visit.
Your question about Helsinki is a good one. I would say that you'd have to asterisk it if you describe it as a visited place. "I spent a day in Helsinki, but I can't say I properly saw it" (But, then again, I spent four hours in Cancun once, and fled, appalled. I count it as having been there.) Your Kenya trip, if I were to have done it, doesn't count. If you didn't actually put any shoe leather down in the area. It's dicey. Another asterisk.
I think it all comes down to a case by case basis. If you feel like you able to get any kind of sense of a place by the time you spent there, I guess you can call it a visit.
[ Edit: Edited on 11-Mar-2018, at 11:46 by Piecar ]