All that has changed. Even Microsoft is starting to build the venerable Microsoft Office suite as a service instead of an old-style application.
What does that mean?
It means, fundamentally, that you should quit thinking in terms of documents and start thinking in terms of transactions. When you create a blog entry for your weblog, you're not "editing a document", you're posting a transaction to a database. The old way of doing this was to open your existing "web page" as a document in a "web page editor" like FrontPage or Dreamweaver, "save" your document with the new text it it, then "upload" the document.
All of that is out the window.
The word "server" is old-fashioned, but it's the closest word we have at the moment. What it really means is that your information is centralized or, as a better way to phrase it, "in the sky somewhere" and you access your data over the network, interacting with it in a series of transactions.
That makes the "server" into the "application", because that's where your data is being maintained, and it's the server that's doing the work of editing it. You're editing it by remote control, through a transaction metaphor.
What this means is that all document-centric software will be history relatively soon. I mean all of it. The idea of "open" and "save" will just go away. Photoshop will have to learn how to edit photographis transactionally over a network, rather than loading the whole thing into memory and "saving" it. Word will learn to edit text through transactions to a remote database, not a monolithic document model.
The nay-sayer in you is saying that this will never happen, yet it is already happening. Web pages are increasingly built through this model, because they are already in the sky somewhere, so the whole round trip of download-edit-save-upload makes no sense. Other document types will follow, until there is no such thing as a document or even a "file" any more.