We study F-saturation games, first introduced by Füredi, Reimer and Seress [4] in 1991, and named as such by West [5]. The main question is to determine the length of the game whilst avoiding various classes of graph, playing on a large complete graph. We show lower bounds on the length of path-avoiding games, and more precise results for short paths. We show sharp results for the tree avoiding game and the star avoiding game.