If you require code that will run on Xbox 360 or Zune then you need a 100% managed engine.

Most of these are free, or are free wrappers around commercial products. You should look at each one and determine pricing and licensing.

• Farseer - 2d only. Source and Silverlight port available
• JigLibX - Source available, port of C++ JigLib, formerly JiggleX
• Bullet 
  •  BulletX: By XnaDevRu: Supports Xbox360 as well as windows. Updated recently (dec 21 2007).
  •  XBAP: By Chris Cavanagh, buildt on BulletX above.
• Newton
• Oops! 3D Physics Framework
• Bepu physics - commercial but free for non commercial use
• Jello Physics - soft body physics. Used in JelloCar and other fun Walaber games.
• Physics2D.Net - see demo video

If you are only targetting windows then you can use any of the commercial, or open source engines. Some have managed wrappers or you may need to roll your own

• PhysX
  • MS Robotics Studio has a wrapper but check the license.
  • http://code.google.com/p/physxdotnet/
• ODE (Open Dyamics Engine)
  • XPA (XNA Physics lib): XnaDevRu has a nice wrapper for, but it's majorly outdated and ODE is rumored to be bad/unstable. There's very little information about it, but the API is pretty friendly. Pretty easy to get up and running with simple collisions (even I made it!), but its hard to find what you need when problems occur, and its updated very slowly.
• Newton Game Dynamics
  • [link appears to have died] Newton physics: Was written in 8-10 hours so I guess its quality reflects that.

Other Lists
XNAWiki Physics Engine list

Ziggyware Physics links