This thread is almost in three different directions. As a pro/entertainer, as a player with a passionate interest, and as a person with an instrument in a group of people. I think the answers are different in each case and each has been addressed to some degree.

Cranky does a good job on one and I think we all have some personal preferences if someone just "wants to hear you play." I think the third is much like having your instrument (esp a guitar or banjo) in some social situation like camping. When people want you to play then, you can probably get off a tune or two before they get bored, because in many cases what they really want to do are things they know. In those cases, I find it a lot more fun to play whatever it is and have fun. You might even be able to teach them a "new one" that you like.

Spaw