At the top my list, even if it might not technically be a board game: Mah-Jong. The most complex part of the game tends to be the scoring, and agreeing on a set

At the top my list, even if it might not technically be a board game: Mah-Jong. The most complex part of the game tends to be the scoring, and agreeing on a set of rule variants your entire gaming group don't object to. After that, Scrabble and Puerto Rico.