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/Peo, FreeWebSpace.net
Absolutely! In fact, that's the recommended method. Buying your domain from your host isn't the best plan, as if your host goes under or doesn't care for you anymore, there goes your domain. And GoDaddy's hosting is horrible.
Yes it's definitely possible. You just have to change the nameservers of the domain which you bought at GoDaddy and point them to your hosting provider.
I did not found any domain registar who would not allow you to point your domain to different hosting provider.
You just need to change so called nameservers or DNS. Nameservers you will receive from your hosting provider.