I take pride in my independence and competence and if I have to ask for help too much, it takes away from that, and ultimately part of my self-esteem. I like to do as much myself as possible but I've come to learn that there are going to be times when I'm stuck on a problem and that asking for help is okay.
There's a big difference between asking for help and having someone do it for you. If I'm not sure how to do something, I like someone to walk through the process with me so I can do it all on my own next time. The only time I would ask someone to do something for me would be in the case where I was physically unable or really sick. For example, have someone very strong lift a really heavy object or have someone do errands if I fell very ill.