I never regret anything. Because every little detail of your life is what made you into who you are in the end. - Drew Barrymore 
As much as I adore Drew Barrymore, I think this is a load of horse hockey.
It's a fairly popular sentiment, though. Usually a conviction given by someone who is noticeably wiser and more mature, looking back over past mistakes, and how the repercussions of those mistakes changed them, making them the person they are today.
Read more: http://www.blogos.org/thetakeaway/regret.php