it depends on game...
my true gaming era ended arond 5 years ago...since then im able to find only a very few games that really impress me (half life series, portal, mass effect,...)
in that time, i played baldurs gate and fallout 1 & 2 (3 sucks hard) a lot and those were games i played maybe 5 times in a row! i tried to know every detail, do all quests, properly finish each dungeon.
in all games i play i want to know the plot, when plot is shitty, my interest in game falls down...games like cod:mw or bf were just ...play, click, save, load, kill, ok uninstall
if i want some psycho action, i install unreal tournament and play online
operation flashpoint 1 was amazing tactical wargame, where you had to think a lot what to do; i also tried dragon rising but it was just BORING
i dont like how games try to look awesome, but thats all, i love games where im part of good, original story (except the portal of course)