"Design patterns are recurring solutions to software design problems you find again and again in real-world application development." (www.dofactory.com). Using design patterns in your code provides structure, good practice, familiarity for other developers, and greater confidence that you're doing it "the right way".
In my experience, many .Net developers have never needed to consciously use patterns because .Net is simple yet powerful enough to get away with it. However, as clients demand better applications, design patterns are becoming almost required.
The groundwork for design patterns is the 23 described in Design Patterns: Elements of Reusable Object-Oriented Software by Erich Gamma, Richard Helm, Ralph Johnson, and John Vlissides (the "Gang of Four" GOF). data & object factory provides a convenient, online, C#, reference for these on their website: http://www.dofactory.com/Patterns/Patterns.aspx. Steven John Metsker also wrote the book Design Patterns in C#, which covers these standard patterns using C#.
Moving beyond the GOF patterns, Microsoft's Architecture website provides many enterprise patterns for enterprise applications: http://msdn.microsoft.com/architecture/patterns/default.aspx?pull=/library/en-us/dnpatterns/html/ESP.asp
The more I use patterns, the more I like them.