Taskbar + Start menu settings > Start menu tab > Customize > Advanced > Start menu items > Run Command.
Alternatively you could use the keyboard shortcut to get the run box by pressing WinKey + R
A. Open Windows Explorer and navigate to the "C:\WindowsSystem32" directory. Within this directory, locate the "gpedit.msc" file and double-click on it. This should open up the Group Policy Editor. Navigate to "User Configuration -> Administrative Templates -> Start Menu and Taskbar". On the right side of the screen, locate the policy labeled "Remove Run menu from Start Menu" and double-click on it. Set this policy to "disabled". Click the Apply button, followed by the OK button. Within a few minutes the Run option should become available again.
This set of instructions will work on Windows XP Professional Edition, but I am pretty sure that the GPEDIT.MSC file is not available on Windows XP Home Edition. If this is the edition you are on, then go to "Troubleshooting Windows XP, Tweaks and Fixes for Windows XP" and locate the link labeled "Restore the Run Command". This should provide you with a file that you can run and merge to your registry. I trust this ... site, but you might want to take a look around it before you download and run this file. Merging anything to your registry is a risk, so it is always a good idea to make sure that you personally trust the source.