<p>Most of the work I do is with what could be considered enterprise Web applications. These projects have large budgets, longer timelines (from 3-12 months), and heavy customizations. Because as developers we have been touting the idea of the Web as the next desktop OS, customers are coming to expect the software running on this "new OS" to react the same as on the desktop. That includes easy to manage automatic upgrades. In other words, "An update is available. Do you want to upgrade?" Is this even a realistic expectation? Can anyone speak from experience on trying to implement this feature?</p>

One of the primary reasons to implement an application as a web application is that you get automatic upgrades for free.  Why would users be getting prompted for upgrades on a web app?
For Windows applications, the "update is available, do you want to upgrade?" functionality is provided by Microsoft using ClickOnce, which I have used in an enterprise environment successfully -- there are a few gotchas but for the most part it is a good way to manage automatic deployment and upgrade of Windows apps.
For mobile apps, you can also implement auto-upgrades, although it is a little trickier.
In any case, to answer your question in a broad sense, I don't know if it is expected that all enterprise apps should make upgrading easy, but it certainly is worth the money from an IT support standpoint to architect them to allow for easy upgrading.