It appears there is a difference between setting up styles inline and setting them up in a stylesheet. When using the HoverMenuExtender, the panel that appears when moused over will display briefly, unless you specify style="display:none" on the panel (hide it by default). The HoverMenuExtender goes to the step of hiding the panel for you, but it doesn't happen right away, and all of the mouse over panels appear briefly.
I have a CSS class style for these panels, and I tried to put display:none in there. But I had additional consequences with that; text within the panels wrapped at wierd times, unless there was an inner control laying out the content. The solution was to remove display:none from the CSS style and put it in the style property of the panel, and that worked, for whatever reason that may be.
It may seem like with all of these new technologies, that Silverlight and AJAX will replace ASP.NET as the way to render content over the browser. However, that is kind of a misnomer, because Silverlight and AJAX are technologies meant to enhance ASP.NET, rather than replace it. For instance, all of this is meant to work within the realm of ASP.NET pages, and using the same existing plumbing as was available before, but providing an extra layer over top of it all. In addition, the AJAX extensions provide some additional services that it uses to provide the services it does.
However, it's not meant to replace this. Silverlight is very handy tool to have, but in my personal opinion, its usage is to enhance ASP.NET applications, at least as of yet. With Silverlight 1.0 not supporting everything that is available in WPF, this can often be a drawback to implement complete functionality within Silverlight's capabilities. Although Silverlight 2.0 seemingly will support many more features, I believe that the industry has too much leveraged in ASP.NET applications. This means that most organizations may use Silverlight to add flash-like presentations, provide advertisements, or increase the attractiveness of the GUI, but it isn't going to replace the major portions of the application.
The AJAX Control Toolkit provides an arsenal of tools available that use the full AJAX features of the framework. As the toolkit develops, you will see more of these leveraged in the industry in applications, and may replace a lot of the standard .NET server control usages. However, most of the toolkit was meant to enhance the ASP.NET server controls, not replace them.
Of course, who knows what will come in the future...