You can get still get Windows 10 remote server administration tools for earlier versions of Windows 10. For anything later than the October 2018 version of Windows 10, the RSAT tools are installable as features on demand. Instead of downloading an RSAT package you go to Manage optional features in Settings and click Add a feature to see the list of available RSAT tools. Select and install the specific RSAT tools you need.
To see the installation progress, click the Back button to view the status on the Manage optional features page.
I am keeping the information below for my own reference, but have removed the old links that are now dead.
The Remote Server Administration Tools for Windows 8 enables IT administrators to manage roles and features that are installed on computers that are running Windows Server 2012 from a remote computer that is running Windows 8.
http://www.microsoft.com/en-us/download/details.aspx?id=28972
Remote Server Administration Tools for Windows 8 can be used to manage some roles and features that run on Windows Server 2008 R2, but has limited functionality managing roles on servers that are running releases of Windows Server that are older than Windows Server 2012. For a table describing the available tools and the versions of roles and features that they support, see Remote Server Administration Tools (RSAT) for Windows Vista, Windows 7, Windows 8, Windows Server 2008, Windows Server 2008 R2, and Windows Server 2012.
The tools include Server Manager, Microsoft Management Console (MMC) snap-ins, consoles, Windows PowerShell cmdlets and providers, and command-line tools for managing roles and features that run on Windows Server 2012. In limited cases, the tools can be used to manage roles and features that are running on Windows Server 2008 R2 or Windows Server 2008. Some of the tools work for managing roles and features on Windows Server 2003.