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.