If everything you cared about was on the web, how would that change your design of the web browser? How would it change your design of the operating system? Would you have a start bar, or a window manager, or a file menu?
What would your photo management software look like? It'd look like flickr, and on your local machine you'd just have something that transferred photos directly from your camera to flickr.
Of course, it makes sense to look at Flock, which seems to take the browser pretty seriously and has some modern amenities.
It would be worth looking at what Tomboy does and think about how a wiki in a web browser could match that functionality and ease of use. Then think about what kind of hooks the browser would need to provide for other web applications to do similar stuff.
One should also look at feedreaders, like FeedLounge. I find the sidebar particularly interesting. What if you had a sidebar that replaced the start bar? One possibility would be to have the history always open, with some frequently visited links above it. Or perhaps have a sidebar more like ?FeedLounge's. Firefox is playing around with vaguely related ideas with their Places menu under development for 2.0.
It's also interesting to look at what is happening with Greasemonkey. Take Greased Lightbox for example. It's totally subverting the the hypertext model, but it's usable, and it's fast (when it works :-P). With AJAX it's clear we've started breaking hypertext, and greasemonkey breaks HTTP. What's not clear is what we are enabling and how to best make use of these new freedoms.
As explained in The Inventor's Dilemma and this Steve O'Grady post, OpenOffice.org's approach will not work. You can't subvert the Office culture by trying to attack it head on with a value proposition. This might work in other areas, but it'll be extremely hard here. And MS is fighting back.
Instead, you need to create a tiny bubble in the market. This is what Writely will do. It won't come in as a replacement for Word, it will come in as a replacement for one Word task. And that one task will become two, and then three, and then before you know it it is ONLY the bizarre macro-riddled documents that people are opening in office. And it's a drag.
Microsoft knows this. It's why they are pushing Windows Live. But the internet is a much harder market for them to compete in, and they will be searching for new venues for vendor lock-in.
This is how web technologies will continue their move towards domination, but what does that mean for this new browser? Am I competing directly with Microsoft? On what merits does MS sell IE?
A special page for tags. It'd open up a full screen view of your tags: flickr, del.icio.us, yahoo my web tagging.
An opportunity for pages to set the URL of the page without reloading.
I need to think deeply about the difference between Ctrl+T and Ctrl+N in Firefox. Sometimes you want to be able to switch back and forth between two things, and then look at some other stuff, and then go back to switching back and forth between those two things. Are Ctrl+N, Ctrl+T, Alt+Tab, and CTRL+PgUp/PgDn really the best way to do this? Kynthia points out that there's a plugin that changes the function of Ctrl+Tab to be more like Alt+Tab.
See Miguel De Icaza's post on similar subjects too. He talks on FLOSS about this too.
Also check out YouOS, the AJAX desktop-in-a-browser for a related, if different, project.
Here's a Washington Post article about the desktop->web phenomenon