BioWare's Casey Hudson, Project Lead on the Mass Effect series, has revealed that by tracking the actions of players in the previous two games, their writers now have "over 1,000" variables to draw upon when shaping Mass Effect 3's plot.
"We plan out the larger plot points of the story from one game to the next," Hudson told PC Zone magazine. "We record what a player has done in a playthrough, and then we have all of those choices available for the writers to refer to as they build storylines."
"Numerically, it's over 1,000 variables we'll have access to for shaping the Mass Effect 3 experience for those who've played the previous game."
As a thought experiment: assuming those variables are at the very least, all binary choices, that gives BioWare a potential number of explicit outcomes of approximately one centillion. Though it's unlikely BioWare's writers will drastically alter the storyline based on whether you did an embarrassing dance on Omega.