Windows 8 will launch any application from the Start screen if you type its name and hit enter. But if you want the familiarity of the Run dialog from older Windows versions, you can add that too.
If you type 'run' onto the Start screen, you'll see it pop up as an app. You can then simply right-click and Pin to Start to have easy one-click access. That said, if you're regularly running apps this way, your best friend remains the Windows-R keyboard shortcut, which instantly pops up the Run dialog.
We've previously shown you how to add a full-blown Start menu to Windows 8, though the process is a little fiddly. I'm really hoping that one of my favourite Windows utilities, Classic Shell, gets updated to run on Windows 8. Classic Shell is an old-school Start menu replacement, and I'm completely habituated to launching apps using it with two quick keystrokes. That's something the new-look Start page simply can't compete with.