These days Mandarin Chinese is growing more and more popular as a second language for people all over the world. This is true mainly because of the evident booming Chinese economy and the current and future market that is growing at a breathtaking pace.
Here are some of the free resources I have come across:
Chinese has four (or five - depending on how you look at it) tones. Here is a page that explains some basic information about the tones in Mandarin Chinese. Also, a link to a Mandarin tone exercise game.
Here is an Audio Tutorial of Survival Chinese
This site has free Chinese lessons.
A fabulous and free online Chinese dictionary.
An assortment of basic Mandarin lessons.
General info about the Chinese language and lots of links to other aspects of Chinese culture, art and more.
Wikipedia info on Mandarin Chinese.
Wikibook on Mandarin Chinese with lessons and information.
I had a synchronous encounter (thanks to a good friend) with someone here in Beijing who is working on a most astounding and incredibly useful project called adsotrans.
From adsotrans read me:
"To use this website simply copy Chinese text into the submission box and click "Adsotate". The text will be automatically annotated -- mouseover any word for a popup with pinyin and english. More control over annotation options and full webpage translation is possible through the advanced interface. If you're simply looking for freshly annotated Chinese texts to read, why not check out our sister site page, which is also open to the public. Students looking for study material should visit News in Chinese."
Indeed, this is a worthy, user-edited and -driven project that is quite impressive.
Their News in Chinese website is a great place for more advanced learners to experience their intuitive user translation interface for reading the latest RSS news feeds in Simplified Chinese from Xinhua. If you are very knowledgable about the Mandarin language, you can contribute greatly to the project with your expertise. Volunteer info is here.
And finally, here are a couple more links for learning Mandarin starting from the basics:
Sinosplice Chinese Language Study Resources
Sinosplice Chinese Study Book Reviews (Great help for choosing a text to use.)
Basic Chinese Phonetics with Pinyin Voice Recordings
Chinese Pronunciation Guide (Requires RealAudio)
There is obviously a lot more info out there, so I encourage you to search around. These links will give a good intro and link to a lot of other sites, but there is so much more out there.
In the words of Mao Zedong himself: "Study hard and make progress everyday." :)