Steven Bristol has a great checklist for moving your domains off of GoDaddy and keeping your site up at the same time:
I don't lose my current DNS settings. Although I want to use DNSimple to manage my dns settings, some of my domains have a lot of configuration and I never had the time to move everything at once. It turns out I don't have to: DNSimple will use your existing DNS server by default if you transfer. Now I can do all of this in two steps, which makes it easier for me.
Could have used this last week.