What's worse is that the problem doesn't lie with your network servers or your clients. Virtually every Windows, Macintosh and Linux device already supports IPv6 in some fashion. Major websites such as Google (http://ipv6.google.com/) and Facebook (http://www.v6.facebook.com/) already have IPv6-specific sites that you can use only if you can access them.
What's missing is the middle part. Chances are, your firewall doesn't work with IPv6. It's also likely that your ISP doesn't support it either. It's even possible that your network infrastructure, such as DHCP servers, switches and other devices don't support IPv6, but in many cases that may just mean that you need to use network gear made in this century. The problem with security hardware and network access is a bigger issue.
Lately, I've been testing a number of firewalls, for example, and I've found that IPv6 support is minimal at best. Some devices don't seem to support it at all. The same is true with ISPs. My experience is that when you call tech support at your ISP, you'll get a long period of silence, and then a confused 'IP what?'
Fortunately, if you're lucky, there are solutions. You can find a provider that supports IPv6 and then dump your old provider. In large urban areas, this can be fairly easy to accomplish. In less urban settings, you may not have a choice of providers.
The same is true with your infrastructure hardware, although in some cases a firmware upgrade is all that's required to make a switch or firewall handle IPv6. But before you go shopping for IPv6-capable networking gear, you should be prepared to insist that the vendor prove to you that it can support IPv6. You're going to need it now that the IPv4 addresses are exhausted. There's simply no point in buying a device that's already obsolete before you even open the package.
Right now though, it may be impossible for your company to adopt IPv6 for external network access, even if you are otherwise ready for adoption. The poor to non-existent support by the hardware community and the near-total lack of interest by service providers create a very high hurdle. And while you can get around it using tools such as Hurricane Electric's Tunnel Broker, this is only a solution if it works with your firewall and routers. Otherwise, until you find a new provider and new hardware from vendors that care about not selling obsolete products, you're basically out of luck. We may be running out of IP addresses, but it may be impossible to do anything about it.