I'd have to say that one of my greatest parties occurred with a couple of hitchhikers.
I really don't remember what the circumstances were at the time other than it was me and someone else rumaging around Raque Island when lo and behold, Snafu, Avis, and Iceblink appeared in my backpack. Snafu kind of served as my "conscience (as much as he possibly could)" and guided me around the island.
One of my other favorite parites was a wizard party that I got to lead with about 15 other wizards. I forgot for whom we did the quest, but someone hadn't done Secret Police, so we decided to get someone a membership. It was a fun trip, though we did suffer many deaths. Quite fun, nonetheless.