Wine offers some support for running .net programs. See the .NET AppDB page for tips and to share user experiences.

Quick start:

To install the .net runtime, use winetricks to install the appropriate Microsoft .NET runtime (dotnet30, dotnet20, or dotnet11).

You can also use winetricks to install the latest Mono .NET runtime (mono22), but that only works for 'pure' .net programs at this time. (See also Mono-Wine_bridge.)

Be advised that although its possible to install .net runtimes, your application probably might not work (yet). Also, the Microsoft .NET runtimes are not Free Software; read their EULA before accepting. (Mono is Free Software, so if it meets your needs, it's a better choice.)