Not an answer for 4.0, but worth noting that in .Net 4.5 you can make this even simpler with:

#pragma warning disable 4014
Task.Run(() =>
{
    MyFireAndForgetMethod();
}).ConfigureAwait(false);
#pragma warning restore 4014

The pragma is to disable the warning that tells you you're running this Task as fire and forget.

If the method inside the curly braces returns a Task:

#pragma warning disable 4014
Task.Run(async () =>
{
    await MyFireAndForgetMethod();
}).ConfigureAwait(false);
#pragma warning restore 4014

Let's break that down:

Task.Run returns a Task, which generates a compiler warning (warning CS4014) noting that this code will be run in the background - that's exactly what you wanted, so we disable warning 4014.

By default, Tasks attempt to "Marshal back onto the original Thread," which means that this Task will run in the background, then attempt to return to the Thread that started it. Often fire and forget Tasks finish after the original Thread is done. That will cause a ThreadAbortException to be thrown. In most cases this is harmless - it's just telling you, I tried to rejoin, I failed, but you don't care anyway. But it's still a bit noisy to have ThreadAbortExceptions either in your logs in Production, or in your debugger in local dev. .ConfigureAwait(false) is just a way of staying tidy and explicitly say, run this in the background, and that's it.

Since this is wordy, especially the ugly pragma, I use a library method for this:

public static class TaskHelper
{
    /// <summary>
    /// Runs a TPL Task fire-and-forget style, the right way - in the
    /// background, separate from the current thread, with no risk
    /// of it trying to rejoin the current thread.
    /// </summary>
    public static void RunBg(Func<Task> fn)
    {
        Task.Run(fn).ConfigureAwait(false);
    }

    /// <summary>
    /// Runs a task fire-and-forget style and notifies the TPL that this
    /// will not need a Thread to resume on for a long time, or that there
    /// are multiple gaps in thread use that may be long.
    /// Use for example when talking to a slow webservice.
    /// </summary>
    public static void RunBgLong(Func<Task> fn)
    {
        Task.Factory.StartNew(fn, TaskCreationOptions.LongRunning)
            .ConfigureAwait(false);
    }
}

Usage:

TaskHelper.RunBg(async () =>
{
    await doSomethingAsync();
}