I\'m getting to the point on an app where I need to start caching things, and it got me thinking...
Persistant private data storage.
You need a server to store data with various levels of public/private access. You also need a server for secure closed source information. You need a server to do heavy lifting that you don't want to do on the client. Complex data querying is best left upto your database engine. Indexing and searching is not yet optimised for javascript.
Also you have the issues of older browsers being far slower. If your not running FF4/Chrome or IE9 then there is a big difference between data manipulation and page construction on the client and the server.
I myself am going to be trying to build a web application made entirely using a MVC framework and template's but still using the server to connect to secure and optimised database.
But in general the application can indeed be build entirely in javascript and using templates. The various constructs and javascript engines have advanced enough to do this. There are enough popular frameworks out there to do this. The Pure javascript web applications are no longer experiments and prototypes.
Oh, and if were recommending frameworks for this, then take a look at backbone.js.
Security
Let's not forget that we do not trust the client. We need serverside validation. JavaScript is interpreted, dynamic and can be manipulated at run time. We never trust client input.