The main reason for approving comments would be the obvious reason: To keep negative and hateful comments off of your positive space. This can also help from a full on brawl happening on your blog for the whole world to see. I don't know about you, but that can't be fun for anyone. If your blog is your business or something you do to earn a means of income, keeping it positive and clean is the best way to go.
The next reason I found very helpful is that I DON'T miss any comments anymore. I have to physically approve all of them. To make sure I don't miss them I normally reply to them before I go on to the next. It makes it so much easier and less time consuming for me to get back in touch with everyone.
The last reason I believe helps when approving comments is the ability to have all the info in front of you. You can see all of the negative comments, which includes e-mail address and ip address, so if you want to report it you have it all right there without having to weed through all of your comments to find them. You can also see all of your happy positive comments right in front of you. I don't know about you, but that sure makes my day!
Do you approve your comments? Why or why not? I'd love to hear your comments on this!