If you can find some good 64-bits versions of your popular software then yes, upgrading to 64-bits will be an advantage. And there are 64-bits versions of certain applications available. However, these applications tend to be related to image manipulations, movie editing and of course sound editing. Basically, just applications that will handle loads of data. The quality of watching a DVD movie on your PC will also increase since the system can handle the data a bit faster and it can store more data too, if your system has more RAM available.
There's also a small performance gain if you tend to run lots of applications simultaneously. (Even if all those applicatuions are 32-bits versions!) Why? Because the OS itself can handle the additional memory a bit easier, thus allowing more applications to stay in-memory which results in less swapping to the swap file. (And you can have a lot bigger swap file too!)
But I upgraded to 64-bits because I do a lot of image manipulations, which requires a powerful system and lots of memory. (Well, I need a lot of memory, at least.)
1Good question, I've been thinking the same. Maybe you should clarify what sort of person you are trying to convince, because some of the answers below would be far too technical if we are talking about a casual computer user. – Ash – 2009-07-20T11:52:09.893
1ashh: that is because the benefits and drawbacks of 64-bit operating systems are all very technical. At least on Linux, for nontechnical end users there is almost no noticeable difference (even I constantly forget whether the machine I'm using is a 64-bit or a 32-bit one); on Windows, there are more incompatibilities and oddnesses to deal with on 64-bit, but other than that again a nontechnical end user will hardly notice the difference. – CesarB – 2009-07-20T14:19:31.910