After July 14, Microsoft will no longer issue security updates for any version of Windows Server 2003. Mainstream support ended in July 2010, so the writing's been on the wall a long time. That means you should have already started, if not finished, your migration to a more current version of Windows Server.
But many businesses haven't done anything to move from Windows Server 2003. In fact, many seem to have decided to remain on Windows Server 2003 sans security and maintenance support. That's irresponsible, and you know it.
You've had 12 years of updates and patches, so the old "it's not fair for me to have to pay for a new server OS" argument is getting tired at this point. All software (whether paid or free) needs to be updated at times. And a dozen years of support is generous.
It's time to either make the move to a new version of Windows Server on-premises or to move to the cloud ... or to Linux (just kidding). For most organizations, upgrading Windows Server within their data centers is the cheaper choice.
Because Windows Server 2016 isn't shipping yet, you're probably looking at a move to 2013's Windows Server 2012 R2. Moving from Windows Server 2003 to Windows Server 2012 R2 is an incredible upgrade in terms of Hyper-V virtualization features, security improvements, Remote Desktop Services (an improvement over Terminal Services), Server Core, IPv6, and PowerShell management.
I don’t recommend moving to an earlier version of Windows Server such as Windows Server 2008. Doing so will put you uncomfortably close to its end-of-support period, which will come sooner than you realize, and dump you in the upgrade cycle yet again.
Microsoft has four sets of tools to aid the migration process: Discover, Assess, Target, and Migrate. Inventory your existing environment first, consider hardware upgrades if needed, review software that may not run on a newer version, then actually migrate. If you're worried about application compatibility in the leap from Windows Server 2003 to Windows Server 2012 R2, don't be; it's nothing as major as the application leap on the desktop from Windows XP to Windows 7 or 8.
For assistance in the discovery phase -- to catalog applications and app dependencies -- consider using the Microsoft Assessment and Planning Toolkit (MAP), an agentless tool for inventorying and assessing desktop, server, and cloud migrations. If you use a System Center Configuration Manager (SCCM), you can pull inventory reports from there as well.
I recommend you try the free online tool Windows Server 2003 Migration Planning Assistant. It offers quite a bit in terms of category and workload options that you need to migrate and helps you work through the needs for each. Once you choose what you have and where you'd like to go, the tool responds with tips to smooth that migration.
When you move from Windows Server 2003 to Windows Server 2012 R2, you likely will want to upgrade your server hardware at the same time -- or move to virtual machines. When improving your server OS, it makes great sense to also get better hardware and the efficiencies of server virtualization. After all, you're trying to get as much headroom as possible by making the leap to the current version of Windows Server; don't let your hardware hold it back.
I also recommend upgrading your domain servers if you haven't done so recently. But make sure your Active Directory domain is in order first. The DCDiag utility can help analyze the state of one or all domain controllers in a forest and report any problems. Be sure your forest and domain functional level are ready for the new domain controllers you'll be adding. That means to go as high as possible (in Windows Server 2003) with the functional levels.
Locate your FSMO roles (there are five of them) and be prepared to move these once you have new Windows Server 2012 R2 servers in place. Follow the direction for schema updates before installing the first Windows Server 2012 R2 domain controller using the
Once you've installed 2012 R2 domain controllers, you can move over the FSMO roles and look to demote existing Windows Server 2003 domain controllers using the
dcpromo command to engage the demotion wizard.
If you're starting your migration to Windows Server 2012 R2 or the cloud, you're probably going to miss the July 14 end-of-support deadline. But at least you're moving forward, which is the responsible thing to do.