In my opinion, should not have any regret. Mistakes and failures are lessons.
Sometimes the lesson learned is not worth the price. For example, if you have a kid and regret it, you'll be paying the price for that lesson for the rest of your life or at least until they move out of the house. If you marry the wrong person and regret it, the effect lasts long after divorce. Even some investment mistakes or rather simply choices can have a permanent and life-altering affect on the rest of one's life. I think it's normal to regret things. I certainly do.
I believe that there is a relationship between regret and expectations. Maybe the secret to having a happy life is to have low expectations.