I am currently teaching myelf Hindi, mainly through the book 'Teach yourself Hindi" by Rupert Snell. There are however a few sites where you can learn basic Hindi for free.
The first site is 'A Door into Hindi' which is a wonderful multi-media site featuring videos, audio recordings of native Hindi speakers, transcripts of the dialogues, vocabulary, grammar, etc. The site is broken down into 24 lessons and looks very good. The link is: http://taj.chass.ncsu.edu/index.html
Another site which everyone who wants to learn the Devanagari writing system should explore is the hindi Script Tutor. Again, an excellent tool which shows how to form the characters and how to pronounce them. It can be found here: http://www.avashy.com/hindiscripttutor.htm
Finally there is another website with a free component and a paid subscriber area titled: 'I Speak Hindi'. The amazing thing is that the paid subcsription is $ 12.00 for 6 months or $ 2.00 per month. This site is updated daily with brief topical lessons and vocabulary. Also all lessons are archived for review. It can be found at: http://www.ispeakhindi.com/