What architecture and patterns can I use to share the most model and logic code between a WPF and an ASP.NET MVC application?
I am trying to achieve a bit more here than
Starting with the obvious. Encapsulate your business logic and domain model in a separate assembly.
In terms of Presentation Layers and shared UI Behaviour, the closest you will get is the MVVM design paradigm, implementation will be C# in WPF/XAML and Javascript for your ASP.NET MVC web frontend.
For the web frontend you can get close to the WPF (MVVM) way of doing things with http://knockoutjs.com/ written by Steve Sanderson of Microsoft. Its MVVM for the browser. Also checkout http://www.asp.net/mvc/mvc4 for more info.