Here are a few resources I can personally recommend to learn PowerShell and PowerCLI :

Video trainings :

Getting Started with PowerShell 3.0 Jump Start :
An amazing and fun introduction to PowerShell, filled with eye-opening tips and tricks from Jeffrey Snover, the “inventor” of PowerShell.

Advanced Tools & Scripting with PowerShell 3.0 Jump Start :
The follow-up to the “Getting started” course but it goes into scripting and building flexible and reusable tools with PowerShell. Again, Jeffrey Snover provides invaluable behind-the-scenes insights.

Getting Started with PowerShell Desired State Configuration (DSC) :
Once again, a free MVA course delivered by the enthusiastic Jason Helmick and Jeffrey Snover. It is pretty easy to understand and fun. Again, the participation of the “inventor” of PowerShell allows us to learn the “What” but also the “Why” of many PowerShell DSC features and components.

Windows PowerShell v2-v3-v4 Ultimate Training  :
The most complete video training you could find on PowerShell, it contains dozens of hours of material. Delivered by Don Jones, long-time PowerShell guru and a really, really, great teacher. What is really nice in this training is that topic by topic, it provides the differences and the new features introduced by different PowerShell versions.

Books :

Learn Windows PowerShell 3 in a Month of Lunches :
This book by Don Jones takes your PowerShell knowledge from zero to proficient in all the fundamental concepts. Even if you are already familiar with PowerShell, you will learn a lot with this book.

Learn PowerShell Toolmaking in a Month of Lunches :
Same format and same great author as the book just above. It is more advanced because it goes into not just scripting but building flexible, highly reusable tools which behave like native PowerShell cmdlets. This book teaches widely recognized PowerShell best practices and will make you realize its elegance and its power.

VMware vSphere PowerCLI Reference: Automating vSphere Administration
This book is quite old now, but it is still a reference. The authors (Alan Renouf, Luc Dekens, etc…) are all recognized PowerCLI experts. It features complete scripts, some of them pretty advanced, to automate specific tasks in vSphere. There are probably newer PowerCLI books, but I haven’t read them.
EDIT : The 2nd Edition of this book is out :
It covers all the new stuff : PowerCLI 6.0, vSphere 6.0, SRM, vCloud Air … There is no other PowerCLI book with this breadth and depth of coverage.

Blogs/Sites :

Hey, Scripting Guy! Blog :
Ed Wilson’s blog is the de facto reference, when you google (or bing) any PowerShell topic, chances are, an article from the Scripting Guy will pop up and help you in your quest. :
Community-focused site with “how-to” articles and great to keep up with the PowerShell-related news and events. Also, their forum is friendly to beginners and advanced users alike.

Virtu-Al.Net :
Alan Renouf is Mr PowerCLI within VMware. His scope has expanded quite a bit now, but he is still passionate about PowerCLI and very much involved in the PowerCLI community.

Automating, learning, sharing