I believe that this will affect your application if you decide to take advantage of the new HTML5 features. An application can always make minimal changes to the user interface, as when adding new tags, but there is much more that you can do with HTML5, which will affect how the server code is structured.
Here are some examples:
Your site can continue to work even offline, using new caching features. This means that when the client reconnects to the network, some kind of synchronization is required.
Web SQL databases allow you to structure the storage of client-side data. This can significantly affect the server load. Imagine if StackOverflow.com is only dropping new questions, or twitter.com is sending new messages instead of a document with all the messages with each request. This effectively means that the server will play an increasingly important role as a web service that serves JSON / XML and is less concerned with HTML, Javascript and CSS.
Compiled calculations that were previously frozen in the browser and performed on the server side, because the reason can be uploaded to the client using web workers.
Web sockets can be used to replace Comet and other methods that increase the connectivity between the client and server. However, if your application needed real-time updates, you would already be using Comet, so this change would be minimal.
Image processing and processing can be uploaded to the client using the canvas.
In addition, most of the other changes are related to viewing and should not affect other parts of your application, as suggested by @Jens.
Take a look at these live demos to see what is already possible in modern browsers - http://apirocks.com/html5/html5.html#slide1
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