With respect to personal computing (What do we now call desktop/laptop computing in an increasingly mobile world? Traditional computing? Non-mobile computing?): many of my friends live in their web browsers. They use Gmail and check it through Gmail.com. They either use Twitter.com or some browser-based Twitter extension. They use Google Talk directly. Some daring souls have even adopted Google Docs as their primary document editor. Others, like myself, remain wedded to the world of native apps. I use Apple's Mail.app for all of my mail accounts. I use Echofon and Tweetie for Mac for my Twitter needs. I use Adium to chat. I use Office 2011. And as of today, I use Reeder for Mac (still in beta) for my Google Reader needs.
Unlike many tech topics, I don't have a strong opinion as to which of these two methods is the "right" way of using your computer. They have their advantages and disadvantages, but this is actually an area where I think that personal preference is king. Personally, I enjoy native apps versus browser-based apps for one reason: focus.
When I pull up Echofon, I use it to tweet. When I open Mail, I'm checking email. When I click on my browser, there are a billion things that I could be doing, each of which would distract me from my original objective.
That's what works for me. What works for you?