Best solution to the player introduction conundrum I've experienced was seriously a simple and surprisingly effective solution, which is all of the characters knew each other already and players could mention something that happened in their history (in-game references) that other player characters could fill in the blanks. For instance, 

"Oh, Tom knows all about dangerous caves. He ran into a tiger's den when we were on an exhibition three years ago."

"Hey, you were the one urging us to get out of the rain!"

"Don't forget about the tribe of cannibals that were on our trail, either."

It doesn't have to be predetermined, it can just be spontaneous. You can be surprised by how easy it is to just go with the flow and get into the juicy stuff. Some of my favorite RP moments happened because of situations like that.