Adding scripting functionality to .NET applications
You might be able to use IronRuby for that.
Otherwise I'd suggest you have a directory where you place precompiled assemblies. Then you could have a reference in the DB to the assembly and class, and use reflection to load the proper assemblies at runtime.
If you really want to compile at run-time you could use the CodeDOM, then you could use reflection to load the dynamic assembly. Microsoft documentation article which might help.
If you don't want to use the DLR you can use Boo (which has an interpreter) or you could consider the Script.NET (S#) project on CodePlex. With the Boo solution you can choose between compiled scripts or using the interpreter, and Boo makes a nice scripting language, has a flexible syntax and an extensible language via its open compiler architecture. Script.NET looks nice too, though, and you could easily extend that language as well as its an open source project and uses a very friendly Compiler Generator (Irony.net).
Oleg Shilo's C# Script solution (at The Code Project) really is a great introduction to providing script abilities in your application.
A different approach would be to consider a language that is specifically built for scripting, such as IronRuby, IronPython, or Lua.
IronPython and IronRuby are both available today.
For a guide to embedding IronPython read How to embed IronPython script support in your existing app in 10 easy steps.
Lua is a scripting language commonly used in games. There is a Lua compiler for .NET, available from CodePlex -- http://www.codeplex.com/Nua
That codebase is a great read if you want to learn about building a compiler in .NET.
A different angle altogether is to try PowerShell. There are numerous examples of embedding PowerShell into an application -- here's a thorough project on the topic: Powershell Tunnel