Everybody has an opinion, and yours may differ based on your personal observations and experiences.
I've been working with the .NET Framework since the first BETA in 2000, and I've seen a lot of stuff come and go. The following are what I consider to be my Top 10 List of things about .NET you must learn, going forward with the technology from 2007 on:
1) WCF (Windows Communication Foundation): While WCF is certainly less "sexy" than say WPF / Silverlight, it is going to represent the backbone of solving business problems with .NET going forward from here. Big organizations are starting to embrace it, and it provides a cohesive framework for solving business problems in a distributed, integrated way. WCF integrates Remoting, WebServices, EnterpriseServices and Transactions, WSE, MSMQ, and much more into a cohesive programming framework. If you intend to make it your business to study just one new .NET technology this year, make it WCF.
2) ADO.NET (and LINQ): ADO.NET is how you talk to a data store, and databases are such a ubiquitous part of what you will do as a developer that you have NO CHOICE but to become extremely competent in this area. The next big thing in how to talk to data is LINQ with language extensions and entity objects that "represent" mappings of data and its relationships. If you don't become at least familiar with all this stuff, somebody else is going to eat your lunch.
3) WPF (Windows Presentation Foundation): Everything you learned about Windows Forms, pages in a browser, and UI elements is going to go out the window, because Microsoft has already declared that WPF is the new way we're gonna do this stuff. Its already built in to Windows Vista, and the XPS (XML Paper Specification) is already built into the printer subsystem. Don't hang on to the old- get with the new just as fast as you can get your little tushy in gear! And besides that, WPF is just so friggin' cool, it will knock your socks off in hi-def streaming video!
4) SQL Server 2005 (and on): I understand this isn't really .NET, but then again it really is. SQL Server 2005 hosts CLR integration of managed code. That's not only revolutionary, it provides a power to the programmer that you cannot get on other platforms. You have to learn everything you can about SQL Server 2005 including Service Broker, because it will help you to be a better programmer and problem - solver.
5) ASP.NET 2.0: Even non "web programmers" need to understand how this works. The feature set has grown and matured, and you are looking at dynamic languages, LINQ, AJAX, and much more being integrated into the ASP.NET Framework (not to forget Silverlight - the sexiest technology of all of them!).
6) Security. Developers are notoriously weak on security ("Who cares about permission sets - I'm just a Code Monkey"). Unfortunately, we do not live in a perfect world and there are evil people out there who jump with glee when they can mess up your day. The more you become an expert about security, the higher your pay will be: expert security consultants make upwards of $300 / hr.
7) TDD (Test Driven Development): Unit, regression and integration testing aren't a luxury - if you want to develop robust systems then you must have a test protocol. And to do testing right, you need to study how to write tests and what tests to write. There are several excellent books on TDD and at least one that specifically focuses on .NET.
8) Networking (System.Net and related): Networking -- TCP, UDP, HTTP, FTP, and on -- are an integral part of what you need to know how to do in order to glue programs together and make them be able to talk with each other and your data. The more you know about this area, the better equipped you'll be to make the right kind of choices when you are tasked with creating business logic through code.
9) Threading: When asked to develop a multi-threaded object or to use a ThreadPool, 95 out of 100 programmers who claim to be professional .NET developers fall flat on their faces! You need to study all the threading primitives, know how they are used, be able to use the .NET or a custom ThreadPool, and manage threads in your applications.
10) Learning. That's right, I classify learning as a technology. People need to become smarter about how to learn, and especially, WHAT to learn. Just as you become a better programmer when you learn to use the Google or other search engines more effectively, you become a better programmer when you can detail for yourself what you need to learn to be better at your craft, and write down a plan for implementing that learning process.