Should I use WPF or ASP.NET for my next Web Application development?

Contrary to what the answers from Greg and Tyler say, you can use WPF in the browser in the form of a WPF XAML Browser Application. These do have some limitations over regular WPF applications, so may not be the right solution for you.

As for whether you should use ASP.NET or ASP.NET MVC, that requires more info from you as to what you want to do with your web application. If you go with one of these then you may also have to consider which javascript library you are going to use (if any; for example jQuery is very popular).

Alternatively, depending on the complexity of the application or its UI, you shouldn't discount Silverlight simply based on the client side plugin reason - Silverlight is considerably easier to develop complex apps in and ongoing maintenance is easier, so make the decision on the whole picture rather than just part of it.

Your options are using ASP.NET web forms and ASP.NET MVC. WPF does not come into play here, it's for desktop applications. ASP.NET and WPF are completely unrelated.

Either way, you have to use ASP.NET.

I strongly recommend .net MVC with the new view engine called razor. this allows you nice separation of layers and can you leverage a lot of front end technologies like jQuery without all of the heavy controls that webforms brings to the table.

I view WPF a lot like flash and sometimes that is the best way to go but for most web apps I would say should be MVC. You can also find support easily for this either for the entire app or just for certain layers of the app.