The Farseer Physics Engine is an open-sourced 2D physics engine designed for Microsoft’s XNA and Silverlight platforms. The Farseer Physics Engine focuses on simplicity, useful features, and enabling the creation of fun, dynamic games.

Demos 

• Feature Demos
• Throwing People

You'll find more samples in its SDK download.

Features

• General
  • Easy To Use!
  • Support for XNA (XBOX 360 and Windows)
  • Support for Silverlight (1.1 and above)
  • Support for Managed .Net Languages In General
• Collison
  • Concave and Convex Polygons Supported
  • Multiple Collision Geometries Per Body
  • Collision Categories For Complex Interaction Between Physics Objects
  • Collision Callback Mechanism
  • Multiple Broadphase Colliders: SelectiveSweep, SweepAndPrunde, BruteForce
  • Line-Line, Line-AABB, and Line-Geometry Collision Methods
• Dynamics
  • Joints
    • Revolute Joint (body to body or fixed to world)
    • Angle Joint (body to body or fixed to world)
    • Slider (Prismatic) Joint
    • Pin (Distance) Joint
  • Force Controllers
    • Linear Spring
    • Angular Spring
    • Fluid Drag and Buoyancy Controller.
    • Easy To Build Custom Force Controllers (Explosions, Steering Behaviors, etc.)
• Support and Debugging
  • Samples Framework With Samples Covering Most Major Engine Features. (XNA and Silverlight versions)
  • Debug Viewer To View All Major Physics Objects (part of samples framework)
  • User Manual (in progress)