Question: Since there's no longer a taskbar/start menu Control Panel, how do you clear the history of the Run box in Windows 8?

Answer: 
Following are the steps to clear history of the Run box:

1. Go to the Start screen, and type `regedit` and open click on `regedit` to open the **Registry Editor**
2. Navigate to the key: `HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\RunMRU`
3. On the right of the screen, there are keys that contain the recently entered commands on the Run Box. Delete the ones that you want to delete
![Registry Editor](https://i.stack.imgur.com/haPMx.png)
4. Log off and Log back on.

That should delete history from the Run menu.

The UI Way to delete History

1. Type `Clear History` in the **Search** box. Then click on **Settings** on the Charms menu
![Select Delete Search History](https://i.stack.imgur.com/0nmKF.png)
2. Finally select **Delete History** to clear the history
![Delete History](https://i.stack.imgur.com/CkUVV.png)

However, that method deletes more than just the search history of Run Box. It also deletes history from other applications like File Explorer.
You can use [CCleaner](http://www.piriform.com/ccleaner) to erase the run history.

![enter image description here](https://i.stack.imgur.com/XUiBH.png)