Does anyone know of a site where you can build/design your own HTML web page on the site without needing to buy or manage the domain?

Sorry if this question is really 'NEWB' of me. I am not a web expert by any means but what I'm NOT talking about are sites like facebook or myspace but a site where you can completely customize and HTML code just a single page and link to it. Sort of like Reddit where instead of submitting links under each /subcategory/ you can design your own web page with anything you want under your own web folder of the domain but you do NOT need to buy, own or manage the domain yourself. Sort of like a "Website 2.0"....