i have 3:

1) my personal favorite involves one of my best friends who stayed a little too long (15 days iirc) in the philippines and didn't realize it until he was on the way out (i.e. "your visa no good, sir.") and his flight was in final boarding. shortly thereafter, a discussion broke out amongst the officials and my friend pondered his plight. should he show them some green? how much? then, in a rare moment of courage, he decided to take advantage of the situation and made a run for it.... straight to the airplane lav.... where he remained until after the doors had been shut (maybe take-off, that detail escapes me).

2) my ex-gf was also a poor student in visa interpretation class and managed to stay 45 days longer than chinese offered. at the airport, she was asked to pay nearly $3,000. as a student, she didn't have that sort of cash on her and the officials sympathized so they reduced their demand to $600. while that was also beyond her means, the ensuing commotion attracted the attention of a number of passersby who came to her aid on the spot so she could return home for the holidays. she repaid all within several days.

3) my own story is the least exciting, but i shall include it anyway because this is my thread. i was in beijing several years ago on a friday afternoon and had a visa that was expiring the following sunday so i went to the visa office to get an extension. however, i didn't leave my passport because i was going to shanghai the following monday and the psb lady told me i would have no problem doing my extension there as long as i mentioned her name. so, i went into the shanghai visa place the tuesday after i returned to shanghai only to hear very different advice (shanghai folks aren't too fond of beijing bureaucrats). i must have come across as a bit antagonistic because i got the special backroom treatment. fortunately, as i was interogated, my friend dave continued to work the lady in the front (heaped on lots of praise) and shen eventually burst into the special room with a face saving story and made everything good. paying up wouldn't have been that big a deal (only 2 days), but i was grateful to get away nonetheless.

now, i'm much more careful about visa extensions, as are my 2 friends.

I haven't yet traveled to a country that requires visas for US citizens, but I'd sure like to do so one day soon.

As for overstaying my welcome at a friend's house, I think I've been guilty of that several times.

perhaps i missed used the term 'visa', but i meant to include all those passport stamps that say "visitor permitted to remain until MMDDYYYY".

Having been in to the USA from GB recently, i was supprised on my arrival home to find that the 'stub' from my visa waiver was still in my passport. Does this mean i am still 'officially' in the US as immigration dont have evidence of my leaving the country?.
Will that cause me problems when i return to the US?

We overstayed our visas in Iran. As a result we had to go to a kangaroo court of local mucky mucks and pay a bunch of money. It was a little scary but I was too young to understand the ramifications of such foolishness

We didn't overstay, but violated the geographical restrictions of a visa or whatever the proper name of the permission was at the time.

In the 1970s I was a teenager with my family when we (U.S. citizens residing in West Germany) visited West Berlin by driving across what was then East Germany. We were permitted to drive only on the approved route. Deviating from the designated highway, we were told, could result in imprisonment (in a communist country, no less) for an undisclosed period.

We got to West Berlin safely, and even (under a separate permission, I believe) crossed over into East Berlin for a day trip. Going into East Berlin I remember registering our visit with the American military (or maybe an office of the embassy) at Checkpoint Charlie before we got to the East German guard station and went through their entry procedures, because, as it was stated at the time, if we did not return at our designated time, they'd send the tanks in after us (surely they would've first ascertained the need for tanks before such an action, but that's not the way I remember it being presented at the time). When we got to the East German guard station, we perceived it as a fairly stressful situation. The stressfulness was not measurably decreased when the East German guards came to search the car and discovered that my father had locked the keys in the car. They were not able to see the humor in the situation. Anyway, we completed our visit to East Berlin and returned on time, so no real problems there.

But then, when we left West Berlin for our return drive through East Germany, we got back on the designated road and began the trip home. If you haven't driven in Europe, you should know at this point that in Europe you navigate primarily by following signs to cities or towns that are in the direction you want to travel. Road numbers are often not reliable navigation aids (it's better now than it was then). And East Germany followed this convention, too. The problem was, we didn't see signs to the town where we crossed the border, or to any other city we recognized. So we were driving "blind" for a while, wondering if we were on the right road (we were). Then we saw a sign to a city (we thought) we recognized. We followed the route to that city for a good long while, confident we were on the right road (we weren't) until we came to a sign that said "Warzwa 700km" and discovered we were heading east, toward Poland. We had gotten lost because, since East Germans were not allowed to travel to West Germany, the signs didn't refer to any of those cities. So here we are, deep in "enemy territory" and completely defenseless, as well as having no real idea how to get back home. We drove along in terror for a while, and finally came upon an East German police car stopped on the side of the road. With prayer aforethought, my dad pulled to a stop behind the policeman, got out, and explained our situation honestly, pleading stupidity (he could speak German pretty well). Our prayers were answered when the policeman mercifully showed us where to turn around and mapped out the route home for us, with no fine, no hard time in the Soviet gulags, and no torture to extract the secrets we carried as spies.

Another story happened to a friend of mine, also an American teenager living in Germany in the 1970s.

He was an excellent snow-skier, but evidently not such a good navigator, as he was skiing in Austria one day and took a wrong turn and ended up in a German town on the wrong side of the mountain without his passport (this was before the EU eliminated the need for passports at the German/Austrian border). He found a cab driver who agreed to take him back to his family's lodging in Austria. At the border, the cab driver reportedly made a simple wave of the hand to indicate to the border guard that my friend was yet another idiot skier, and he was passed through without any trouble over the missing passport.