Hieko Seeberger has recently started blogging on functional programming and category theory applied to Scala. Two opening posts are very educative (and easy to read), and can help getting over the initial barrier in learning scalaz.
EDIT: When you get comfortable with the fundamentals, I would recommend you to read through http://apocalisp.wordpress.com/ (blog driven by Runar Oli and Mark Harrah) and the weblog of Tony Morris
UPD: "Functors, Applicative Functors and Monoids" chapter of "Learn You a Haskell for Great Good!" has a lot of examples in Haskell with detailed explanations, which can easily be translated to Scala/scalaz.
I wrote a series of posts on my blog on this topic, and then compiled it together:
There are also some video resources I have seen presenting scalaz at an introductory level,
They are both given by contributors to scalaz and introduce the contents and concepts illustrated by evolving a series of code examples. The audiences for both these talks were Scala enthusiast groups.
I have found this notes interesting:
http://debasishg.blogspot.com/search/label/scalaz
Not tested myself, but maybe this Scalaz Guide can help, initially written in November 2010 (and/or can be contributed to, since it is no longer maintained since mid-2012).
A couple more resources.
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