<p>In other words, is this Singleton implementation thread safe:</p>

<pre><code>public class Singleton
{
    private static Singleton instance;

    private Singleton() { }

    static Singleton()
    {
        instance = new Singleton();
    }

    public static Singleton Instance
    {
        get { return instance; }
    }
}
</code></pre>

The
Common Language Infrastructure specification
guarantees that "a type initializer shall run exactly once for any given type, unless explicitly called by user code." (Section 9.5.3.1.) So unless you have some whacky IL on the loose calling Singleton::.cctor directly (unlikely) your static constructor will run exactly once before the Singleton type is used, only one instance of Singleton will be created, and your Instance property is thread-safe.
Note that if Singleton's constructor accesses the Instance property (even indirectly) then the Instance property will be null. The best you can do is detect when this happens and throw an exception, by checking that instance is non-null in the property accessor. After your static constructor completes the Instance property will be non-null.
As
Zoomba's answer
points out you will need to make Singleton safe to access from multiple threads, or implement a locking mechanism around using the singleton instance.