How Do You Choose a Domain Name?

So, how DO you choose a new domain name? Do you search endlessly for the right combination of words? Do you use a domain name generator? Do names just pop into your brain? Do you scribble idea combinations on a piece of paper?

I always wonder how people come up with such creative ideas for their domains. I own about 8 domains (of which I use 4), but have heard of people owning hundreds! Mine certainly are not overly creative and I think I might want a really cool domain very soon! Any ideas?

Which domain name company do you recommend? Have you tried Go Daddy?