this hasn't happened to me (yet!), but another phd student in my dept did once get invited ( along with a number of others) to her first supervisors house for dinner/drinks. she was only in her first year at the time and was very nervous about it, but went anyway. after dinner, they got the karoke machine out, and every single person there had to do at least one song! she was really embarrassed, and although she now admits it was a good laugh, at the time she just wanted to run away! as a result, it's my goal over the next three years to avoid all such occassions!
also, at our dept christmas party, they make us play all sorts of games, which often end up in you seeing your supervisor (or them seeing you!) in a way you'd really rather not! i don't know the name of the game, but one involves a row of people standing with their legs apart, and others have to crawl through this tunnel to get to the front - which ends up in lots of photos of people in the unfortunate position of crawling through their supervisors legs (or the other way around!) all the females in the department quickly learn after the first year that this isn't an event you want to be wearing a skirt to!