Great White Whale?
There are a lot more mobile phones in the world than there are desktop or laptop computers. Many of these phones have web browsers of one sort or another. But web pages and other web content is designed for desktop/laptop use, for the most part.
Some people think sites should be designed for use on mobile phones (or mobile devices, to be politically correct). On the other hand, maybe mobile devices should be able to (or aspire to) display web content designed for full-size computers. In this way of thinking, mobile users shouldn’t have to operate in an internet “ghetto” containing only “mobile content”.
This argument is still raging. Mobile devices are slow (compared to full-size computers), have tiny displays, limited interaction, and far less storage space to work with. Given these limitations, maybe it makes sense to have a special version of your website for mobile use.
But mobile devices are constantly improving in speed and storage, and lots of developers at Nokia (and elsewhere, believe it or not! 
are working on better ways to display and interact with information. So maybe it makes sense to have a mobile device that works with the main (or only) version of your website.
I don’t have the answer to this, but I do have a suspicion. Smaller, less capable, limited versions of things generally related to computer and communication technology don’t seem to have held up very well over the past few decades. Hardware always gets more capable and less expensive. User Interfaces have been progressing more slowly recently, but still they progress.
I think it’s also a human tendency to prefer the “real” version of something over a simplified, abridged, or reduced version. I could be wrong about this, of course; people do prefer easy/simple/clear to difficult/complex/confusing. I think most people would simply prefer one version of a website, book, movie, database, or what-have-you, but that single version should be useful.
The S60 browser is an attempt to take that way of thinking into use. There are other ways of thinking, and so there are other browsers. If you’re interested, here are some links:
The .mobi top-level domain
The WAP Forum, now subsumed under OMA.
Shakespeare made, um, shorter.
Condensed Books — maybe this could only come from the US!
W3C’s thoughts on Mobile Web Best Practices.
One word (well acronym really): RSS
It doesn’t matter what device you read the data on, the information is portable.
Do I wish I could watch youtube on my Nokia E61? Absolutely! Do I understand the technical limitations? Yes.
When you develop a site for the “web”, it should work on the “web” — not matter where the “web” is. There should only be one web; developers shouldn’t have to make seperate versions of their sites for desktop, mobile, Wii, etc.