Most Complicated RPG owned: Pathfinder, I only own some PDF's but it is extremely crunchy
Favorite House Rule: Rule Zero, and make it up as needed.
I finally ran an adventure in my new campaign setting with my wife, son, and two nephews. It went rather well but I had to make stuff up on the fly. Because I had a sense of the overall history of the setting, the fact my one nephew wanted to be from the future and the other a companion to a time traveling meddler wasn't too disruptive.
The crew meet in the city of Independence, the capitol of the Conclave of Equals. One of the newest nations and certainly not stable or effective with it's tri-cameral legislature and a committee for an executive branch. So far that has not come into play yet, but a gnome is hiring hands to help with a crashed shipwreck. They jump at the chance and find themselves near a druid ship smashed against some rocks. By the end of the adventure they have battled an incubus over a merfolk chest and a dozen merrow(squid like merfolk), and that still doesn't explain how the gnome knew that stuff was there or why there was an incubus involved at all. Perfect for some followup adventures.