I recall Rodgers, back in the Vikings game, where snap was inaccurate which forced Rodgers to retreat into his endzone, stumbling, reaching for the ball, and, while losing his balance, flipped it underhanded as far as he could in an attempt to throw it away.
The result, of course, was intentional grounding. Although I agree with Rodgers' decision here, there are of course situations where you simply cannot throw it away. It's not often as simple as taking a sack or getting an incompletion, as the issue of intentional grounding or illegible receivers compound the issue.
In the above scenario Rodgers did the right thing because taking a sack would have yielded a safety. However, if the QB have not shifted out of the pocket, and a defender is dragging him to the ground slowly, I would prefer the QB to take the sack and protect the ball, rather than try to hobble around and throw while taking a tumble. There's just too much risk in trying to make something out of pretty much nothing.
The real issue in my opinion here is about the timing. Suppose the QB has been brought up to go through his progressions quickly, and, failing to find anyone open, to throw it out of bounds (disregarding the effect of intentional grounding and throwing to illegible receivers). Although this generally means fewer interceptions, there's going to be a whole lot of chances that will never even materialise because the QB never gave the opportunity for a play to develop. Eli Manning probably never would have connected on that helmet catch if it weren't for the fact that he kept the play alive, and they would never have won the superbowl.
But then I think, what would I prefer Rodgers to do? Well at this stage in his career, I would rather Rodgers play it safe than attempt to make too many plays. So, in a way, I agree with both Z2C and MassPack. If Rodgers cannot find someone open, run it or throw it away immediately. Otherwise, if it looks like a sack is inevitable or he cannot get out of the pocket, lie down and protect the football, and
don't try to throw it away.