The title bar and the window border belongs to the non-client area (NC) of the window. If you're writing a message pump based application you can provide your own logic and appearance of this area using the WM_NCPAINT and WM_NCHITTEST window messages (just like Jon wrote).
While this area has been quite moderately used in previous Windows versions, Microsoft has recently (at least since Vista) started to make the non-client area more attractive and feature rich.
In modern applications it is quite common to completely ignore the non-client area and instead create a window that does not have a strict window border and thus consists of ONLY a client area. With this method the window must provide it's own implementation for drawing the window title and window buttons (minimize, maximize/resore and close). Combining this technique with window transparency makes it possible and quite easy to create exciting user interfaces.
If you are using WPF you'll find the WindowChrome class very useful for this purpose. This class is part of the .NET 4 framework and available as a separate library for .NET 3.5.
Edit
Obviously someone does not like this answer. Just to be clear: I'm not saying that this is how Chrome or any other application is doing it. I am saying that how I've described it is a feasible solution which myself and the company I work for has used in several projects and I know for a fact that several other applications use the same approach. It might not be the best, but it is certainly a way to go about it! :-)