Which Lego board games come with minifigures instead of microfigures?
Various minifigures are in included in: 

LEGO Chess Sets: 


Castle - 24 minifigures
Giant Fantasy Era - 33 minifigures
Knight's Kingdom - 24 minifigures
Pirates - 24 minifigures
Vikings - 24 minifigures


LEGO Tic-Tac-Toe Sets: 


Castle - 10 minifigures
Police - 10 minifigures
Pirates - 10 minifigures


Other LEGO Games:


Ludo (a variant of parcheesi) - 16 minifigures
Creationary - 1 minifigure 
Time Cruisers Game - 5
minifigures
Creator Board Game Deluxe - 4 minifigures
Constructionary (a variant of charades) - 2 minifigures
Knight's Kingdom the Game (never released in English) - 5 minifigures