I believe it will have a major impact on your application if you choose to take advantage of the new HTML5 features. The application can always make minimal changes to the UI as in incorporating the new tags, but there is much more that you can do with HTML5 that will affect the ways server-side code is structured.
Here are just a few examples:
Your site can continue functioning even when offline using the new caching features. That means when the client is back online, some sort of synchronization will need to happen.
Web SQL databases can allow storing the data client-side in a structured manner. This can impact the server load significantly. Imagine if StackOverflow.com only pushes down new questions, or twitter.com only sends new messages instead of a document with all messages with each request. That effectively means that the server will play an increasingly important role as a web service which serves JSON/XML and worries less about HTML, Javascript and CSS.
Comlicated calculations which previously froze the browser and were done on the server-side as a reason can be offloaded to the client taking advantage of web-workers.
Web Sockets can be used to replace Comet and other techniques increasing the connectivity between the client and server. However, if your application needed real-time updates, you would already have been using Comet so this change would be minimal.
Image manipulation and processing can be offloaded to the client using canvas.
Besides these, most other changes are view-related and shouldn't affect the other parts of your application as @Jens suggested.
Take a look at these live demos to see what is already possible in modern browsers - http://apirocks.com/html5/html5.html#slide1