I didn't come from a wealthy family and spent all my summers at college working. I was paranoid about trying to avoid debt and was financially responsible for myself.
In retrospect, my biggest regret is that I didn't say "what the heck", took a credit card and some money and just set off on my bike to cycle the continent and just worked out the "details" later. Knowing what I know now, it's something I'd definitely have done (while I have more money now, I don't have the time as I have a family and the USA is miserly with holidays). It's the only big regret I have.
I agree that regretting things is a waste of time, but at the same time it's a human emotion, and sometimes you should just acknowledge your regrets (but of course then move on and preferably learn from them).
EDIT: ooh, ooh, ooh.... just remembered my other thing. My kids always remind me of this. Being an apathetic teenager and turning down a chance to see Queen with Freddie Mercury as I wasn't sure it was what I wanted to spend my hard earned money on. I thought "oh, I can catch him another time, he'll be around....". I must have recounted this story too many times to my kids who always roll their eyes and complain about it!