I've done many things I regret. A ton of things.
I have forgiven myself for a lot of them, but a few still latch on to my thoughts like leeches.
My biggest regret is not taking action when a girl I had a crush on told me that she liked me - Here I am, three and a half years later, having tried (and believed I had been successful in) moving on several times, but still noticing that I have strong feelings for her every time I see and talk to her.
I generally do believe that the past is the past and that there is nothing we can do to change it (until they invent time travel), and thus I think that people should forgive themselves for any harsh regrets that they may have. Any potential god should know I'm trying to do that myself.