Is it possible to make a website without any programming knowledge? Without HTML either? Is there any free or cheap services for this?

You don't need to know much about programming. Get yourself a template and all done! The rest is all about content.

I guess you might need some programming knowledge if you wish to build a database or something, but you can hire someone to do it for you.

The point is - even without programming, you can have a website.

The easiest way around programming is to host a blog. You can install wordpress - a great-looking and well-structured personal blog system(Some web hosting services offer free installation with the hosting package).

With Wordpress you can get free templates and all kind of plugins for it (such as image galleries, stats, anti-spam, comments and much more). Once you have WordPress activated on your site, you will be able to add posts and create pages in no time.

To summarize, without knowing anything about programming, you will have an awesome website.