i believe all the major opensource JS engines (JavaScriptCore, SpiderMonkey, V8, and KJS) provide embedding APIs. The only one I am actually directly familiar with is JavaScriptCore (which is name of the JS engine the SquirrelFish lives in) which provides a pure C API. If memory serves (it's been a while since i used .NET) .NET has fairly good support for linking in C API's.
I'm honestly not sure what the API's for the other engines are like, but I do know that they all provide them.
That said, depending on your purposes JScript.NET may be best, as all of these other engines will require you to include them with your app, as JSC is the only one that actually ships with an OS, but that OS is MacOS :D