Ubuntu 12.10 introduced the "web apps" feature, which promised better integration between the desktop and certain web sites. This feature worked by way of a browser extension, which was only supported by Firefox and Chromium (not Chrome - my browser of choice at the time), and then there were installable add-ons for various popular sites.
Shortly before 13.04 was released I switched from Chrome to Chromium full-time, as I wanted to see what this feature was like to use day-to-day, and then see how it had been evolved in the new Ubuntu release, six months on. After installing 13.04, I was a little disappointed to learn that no changes had been made to this feature at all, as what's there at the moment seems very incomplete.
Looking at some of the extensions individually:
Gmail - The main thing I'd expect from this is new email notification (tied in with notify-osd). For me this worked sporadically (on perhaps 1/4 emails), but it only supports one Google Account (I'm usually logged in to at least two), and there's no way to control which one it uses. No tie-in with the Ubuntu Online Accounts feature.
YouTube - All I really wanted from this one was for it to hook into the OS sound controls, as it would be great to be able to play or pause a YouTube video by hitting the relevant media buttons on my keyboard (like I can with local videos). This one also only worked sporadically, with no obvious pattern as to why.
BBC News - This one I tried but quicky uninstalled. When you load it up it gives you a series of OS notifications for the current top news headlines (almost too quick to read). I can see the thinking behind having a notification when a new 'breaking news' story is posted, but since you need to have BBC News open in your browser anyway for this to work, it doesn't seem that useful.
Reddit - This one has an annoying bug where it incorrectly reads your Reddit 'reputation' score as the number of unread messages. So with this loaded you have a permanent blue 'new notification' icon on your desktop. If you load the app up via. the launcher (giving it its own chrome-less browser window), clicking on self.XXX Reddit links open in new tabs, but external links you click on open in your main browser window, which is a bit confusing.
I also tried the Google Docs and Google Calendar extensions - these didn't appear to do anything. Google Plus I tried - presumably this at least gives you OS notifications for G+ notifications, but for me these are so infrequent that this was tricky to test. Same goes for LinkedIn.
All in all this seems like a missed opportunity. I'm not sure if Canonical made these initial extensions with the hope that the vendors themselves would pick them up and evolve them, or whether these are all just sitting on someone's to-do list somewhere. But as everything moves into "the cloud", there seems to be a lot of potential here to further blur the lines between desktop and online apps, and provide a better experience for the user.
More than any other Ubuntu feature, I hope this gets some love in a future release. In particular, if there's a way to remove the dependency on an open browser tab (with opt-in push notifications for the various services), this could be a really awesome feature.