Engine Nine is the most popular open source XNA game engine that allows you to create amazing 2D and 3D games in C#. It runs on Windows, Xbox, Windows Phone and Silverlight. Licensed under the unrestrictive MS-PL, it is completely free to use with your commercial
or non-commercial applications.
To get started, read the tutorials and documentations. See what other people have said about Engine Nine:

“Engine Nine is breathtaking” –Nelxon

“You are doing some very ingenious architecture work” –TombstonedGuy
Features
Platforms Runs natively on Windows, Zune, Xbox 360, and Windows Phone 7. Runs natively on web browser using Silverlight 5 (Work in Progress). Can be ported to iOS, android though Mono (Future). XAML based content authoring. Graphics 2D sprite, sprite animations and text rendering. Support both forward & deferred lighting Support directional light, point light and spot light. Support shadow mapping and normal mapping. Build-time shader linkage from fragments. Terrain splatting and level of details. Flexible particle system effects and soft particles. Basic primitives: box, sphere, teapot, axis, arrow, point, line, grid. Extensible post processing framework. Built-in high dynamic range, bloom effect, depth of field and blur effect. Animations Skeleton animation, animation blending and custom animation controllers. Full support for Xbox Live Avatar. Transition system for creating smoothed tweening. Physics BEPUPhysics integration.
Donate
Engine Nine is free to download, use and modify. If you find it useful, you can
donate via PayPal or:

Thanks for the donations from:
Tobias Lawrenz Jan Kondelík