Elul thoughts: "No Regrets" was almost a motto for my generation coming of age in the late 60s and early 70s. Probably because we saw too many "lives of quiet desperation" around us, housewives who wanted to be fashion designers, and clerks who wanted to be artists. It's a great hubris: the only way to have no regrets is to never look back. But if you don't look back you don't learn from the past (which studies show is a sign of brain damage). Rambam teaches regret is an important part of teshuva, of turning toward God. We use regret to inspire us to do better, to learn from our mistakes.
The trick is to not allow ourselves to become paralyzed by regret, and not to feel regret over things that happened as a result of influences beyond our control. If you treated someone poorly, you should regret that behavior, and resolve to do better in the future. If your life went in a direction you didn't want because a hurricane destroyed your house, it's appropriate to feel sad, but not regret — it wasn't your fault.
And we don't carry the regret with us forever: we use it to inspire us to move forward, to do better. Come Rosh Hashana we pray that we're on the right track, and come Yom Kippur we know we are forgiven, and we can move forward into the new year leaving regrets behind, knowing we've learned from the mistakes we've made and God forgives us.