"Care about" or "be bothered about", they both could be the meaning of "管" in Chinese. It depends on the situation that you're having. For example, base on your question, "你管我那么多干嘛？" means "It's none of your business! Why do you care about such things?" Or you can say,"管好你自己就行了！", means "Just care about yourself!" So this one could be a little angry.
Well, another way to explain "管", I'll take the situation like you're going to college, and your parents insist on driving you out but just don't need it. Then u can say "不用管我了。", which means "Don't bother."
Hope I can help u~ ;-)