As I conduct research and go on customer visits with IT Administrators from midsize companies, one of the most interesting discoveries has been how little understanding their is around x64 processors. For example, of the 82 customer visits we have conducted, the customers have averaged 11 servers but indicate they only have one x64 server (and they purchase 1.9 servers per year). That math doesn't calculate. NOTE: This isn't the IT Administrators fault, its the IT industry's issue!
I believe some of the confusion can be tied to "64-bit" in general. For lots of people, 64-bit, in the microprocessor world, meant the Itanium brand that Intel created. If you're not familiar with Itanium processors I'll give the 10K foot answer--they are super, high-end specifically meant to tackle the most calculation/memory-intensive workloads. For better or for worse, Itanium also meant a limited set of drivers and Itanium only applications. For example, Windows Server has an Itanium-specific edition. If you have a massive database that can use a terabyte of RAM a Itanium-based server is your answer.
So, what is x64? Microsoft published what I think is good overview whitepaper on the topic and if you're a Wikipedia fan (who isn't?) take a look at their explanation. x64 processors can run a 32-bit/x86 OS without requiring any changes. This is what many customers do today. That is because the processor folks (Intel and AMD) have changed all of their server-class processors from being x86 to x64 without a lot of fanfare. Depending on who you ask, any server-class processor or servers running AMD or Intel processors sold/purchased in the last 18 - 24 months has a high probability of being x64 based.
Why should you care? Windows Essential Business Server will only run on x64 hardware. Windows "7", the next version of the Windows Server operating system will only be x64 (and IA-64). I don't think I'm going out on a limb when I say that within a couple of years all of Microsoft's server applications will be x64 based. RAM is (relatively) cheap and apps love RAM. Heck, long term, I'm sure we'll look back and laugh about running 32-bit apps (remember 8-bit and 16-bit?).
What are the gotchas? The biggest challenge that some people using x64 has been the lack of drivers (specifically print). This issues become less and less with each passing day. FWIW, I'm running Vista Enterprise x64 on my PC and I have very application compatibility problems (e.g. there's no OneNote x64 printer driver) and no driver issues.