You can use any page you like on any website you like as your home page. If I understand your meaning, that's what it's called. Just pick any page on any site you like, and enter it and it will be the default page loaded anytime you load up your browser.

Watch out for google though, as boberonicus says. It's like selling your soul... they've got it stitched up so to get many of the most useful services you effectively (and by default) allow them to track you and collect data on you hugely...