<p>I have a number of web apps running on several IIS6/Server 2003 boxes. They run well and are happy. They are all asp.net web apps and use .NET 3.5.</p>

<p>What, if any, would be valid reasons for contemplating moving the web apps to IIS7/Server 2008?</p>

Eventually, Microsoft will discontinue Server 2003 support. Admittedly, that won't be for several years, so it doesn't impact you today.
Improved support for ASP.NET MVC. This is probably the big one for most of us. You can get ASP.NET MVC working on IIS6, but there are
some hoops to jump through
.
I'd give you more, but I myself am not yet on Server 2008 yet, and have nothing else to give. Presumably Vista (which I do use, both at work and at home) has the "same" IIS7 as 2008 does -- the UIs certainly look very similar -- but I wouldn't consider my experience there to be useful to your question.