Free Chinese Courses

Lessons complete with audio (and/or video), new vocabulary, dialogues, focus on characters and pronunciation

Busuu: a website and an app. A mixture between premium and free. You can learn Chinese by topic and practise vocabulary, and listening. Speaking and writing are recorded and corrected by native speakers. It goes up to Upper Intermediate level.
It's a nice basic tool that you can use on the go. It is not very sophisticated, and this is what I personally don't like about it, I wish there was more to it than individual words.

Practical Chinese Reader with vocabulary lists for it.
This is an entire digitalised course by University of Oxford, where you find texts you can listen to, grammar, vocabulary and exercises. The only drawback is I could not find the key to the exercises, so you don't know if you are doing the homework assignments correctly.

China Radio International
The Learn Chinese section has a lot of information. Lessons in three levels have audio and text that combine English and Chinese and gradually introduce entire phrases in the language.
I like the abundance and the fact that they have more than just plain lessons.
I don't like how messy the website is and how passive it is, as well. The only thing you can do is repeat the phrases, there are no tools for other practice.
Other links: Lessons for beginners, Lessons for Intermediate students
Do explore the site, feel free to click around, there is a lot of good stuff hidden in there under rarely unintuitive design.

BBC Chinese
This is another archived website, but I am including it because I find it has lovely study guides, video to go with the text and even language games.
You can also find interesting articles related to Chinese culture.

Clear Chinese: 15 lessons with basic phrases, audio and practice section.(!The listening is a bit clumsy)

Confucius Institutes Online offer the opportunity to learn about China and its language online. Browse through the website to find interesting articles and online lessons.

I Love Learning Chinese - for beginners

★ Study Chinese with real world video content

Rudgers University: 80 units in 4 levels; lessons in Chinese with English translation and pinyin for the lower levels, grammar and vocabulary explanations for all.

Zhongwen Red: lessons centered around a vocabulary unit that is presented in the context of several example sentences, then expanded upon by a short dialogue, complete with audio.

Overseas Chinese Language and Culture Education: entire levels, complete with a book for the teacher and an exercise book