Please take a look at the CRing Project. Its aim is to be “an open-source textbook on commutative algebra, one simultaneously accessible to beginning undergraduates but advanced enough to cover the foundations needed for a serious study of algebraic geometry”. It just started so this might be perfect if you wanted to jump in and join. Email Akhil Mathew for more information.

Another open source algebra text is Abstract Algebra: Theory and Applications which is run by Tom Judson, Rob Beezer, and Lon Mitchell.

Let me know if learn of others (with relevance to the stacks project).

Could you please say a few words about why these projects were started / the purpose behind these projects. My feeling is that there are already many good books on commutative algebra and on abstract algebra.

You would have to ask the people running those projects. For myself, I don’t think of these projects as books. I love the idea that I am able to rewrite a part of the text, or add something, or get satisfaction from the maintainer if there is a mistake. Also the content of these projects is (and always will be) freely available to everybody.