Being a VB6 programmer, I was looking for a good book to introduce VB.NET. After reading Cornell and Morrison's "Programming VB .NET: A Guide for Experienced Programmers" and Appleman's "Moving to VB .NET: Strategies, Concepts, and Code", I think Troelsen does a better job.
The two previous books are excellent with insight and tips on how VB has changed in VB.NET. (And yes, it's almost a new language.) Yet Troelsen takes the time to illustrate the concepts with very basic code and examples including output. Cornell/Morrison and Appleman have code examples too, but I felt they were cramped for space in their books. Thus, they left out some minor explanations that may make you say, "Aha!" Because of the sheer size of this book, it has plenty of fascinating details to programming with .NET.
By the way, the sample code for all these books are available on-line which is really helpful when it comes to investigating how things work in depth.
Something that stands out is that Troelsen starts with explaining the .NET Platform in detail enough to understand why VB.NET behaves as it does. For example, strings are immutable. Each of these books stresses and illustrates what this means, but Troelsen is the only one that clearly defines why.
Troelsen also writes clearly and concisely; his book is part teaching and part reference. For advanced programmers, perhaps Appleman would be a better choice as he jumps into complex topics and illustrates them with bare-bones examples (as an aside, Appleman is a very colorful writer and he tries hard to make reading enjoyable). For the rest of us with some programming experience, Troelsen goes that extra step to make it easier to understand. For the completely new programmer? While Troelsen does spend some time on the basics, I think some solid understanding of OOP and some VB6 exposure are really required.
Good luck with .NET everyone!