As we get more and more competitive features from Mozilla FF, MS IE8, Opera, and now Google's Chrome the lines between application and the WWW are getting blurrier and blurrier.
When I first started in the hardware business over ten years ago the emphasis was on local process power, RAM, and hard drive capacity. While those are still concerns of a current PC buyer the new "need for speed" is the bandwidth capacity. DSL, cable, fiber, and T1's are all ubiquitous so we just want it faster and cheaper. So what has this done to the modern OS? Not much actually, it has just created more and more applications that live on the world wide web. Oh sure, local PC operating systems will still be utilized for availability and virtualization for managing resources but as more and more applications are written as Rich Internet Applications (RIA), then so too will browsers be equipped for Silverstream, Flash, Java, etc. right off the showroom floor.
The dominant player for Software As A Service (SaaS) is Google and they have gone so far as to create their own browser framework for Google Docs, Gmail, and the like. Even though Microsoft still has the largest market share with IE the other smaller niche open source browsers are quickly on the rise. More and more web users are becoming increasingly aware of security, spyware, and other risks that can break their web sessions, browsers, and even their computers.
In closing, the newest crop of browsers are just touching the hem of the garment of what developers have in mind for our near future personal and corporate applications.