With the move to Internet Explorer 11, Microsoft has dramatically improved the capabilities of its web browser in the Windows Phone 8.1 upgrade. Key among them is the ability to pin a web site to Start as a live tile.
If you're a Windows Phone 8 veteran, you may be wondering why I'm even highlighting this feature. After all, you could pin web sites to Start with IE 10 in Windows Phone 8. But in Windows Phone 8.1, this capability has been enhanced: Now, sites that explicitly support this functionality can provide live tile updates, just like a native app. So they're not static as before.
Of course, the key to this functionality is finding sites that support it. CNN is a good example: With its tile configured for the Large or Medium size, it will cycle through various news headlines.
Windows Phone Central also offers a nice live tile design, though only in the Large tile size.
Unfortunately, there's no way to know whether a site will provide live tile capabilities until you do pin it. My own web site, for example, does not. (And based on the speed at which this company moves, it never will.) So you'll see a thumbnail of such sites on the tile, as you did before in Windows Phone 8.
Pinning works as it did before, of course. Simply navigate to the site, tap More ("...") in the address bar and then choose "Pin to Start" from the app bar menu that appears.
And please let me know if you are aware of any other sites that provide nice live tiles like this.