As someone whose existence crosses the web/mobile barrier, I want to add our experience and conclusions to this thread. I have to provide a little background on us and our users (this is NOT an ad) so you'll see how we got to where we are now.
We run a dating site in the U.S. that provides anonymous text and calling among our members. Our market is those who are tired of the same old email-based dating sites with phony pictures and profiles. Our members want to speak with other members quickly and judge for themselves - if the person is real, fine; if not, move on to the next one.
While we have a full-blown web site, we strongly encourage the use of mobile devices (phones, mostly) for hooking up while in bars and other social venues. Given the limited display area and restrictive interaction for forms and such, to say nothing of the wide range of capabilities, we decided early on to develop two parallel sites with identical functionality; one in HTML the other WML. When we began over a year ago, we hoped to "build once and deploy many times" via CSS, but that just wasn't feasible. I challenge anyone to simply change style sheets and make their site continue to work as well as the non-mobile version when viewed in a cell phone browser. As pointed out by some here, you quickly find that you have to split forms, restrict menu options, limit links, and on and on to accomodate limited browser features. We're not talking PDAs here, but lowest common denominator devices. It is not a mechanical (i.e., CSS) translation; it requires re-thinking the way the user interacts with the device, just as you gave careful thought to the web site.
If you need to make your site available to those with sophisticated mobile devices, especially if you can guarantee that your users all have the same device, by all means use CSS, but understand that even then, it's not a magic bullet that will solve all your problems.
If anyone wants to see what we've got, go to www.zogo.com. Oh yes, you can use a web browser or cell phone equally well.