How to turn off 'Recent Items'/'My Recent Documents' in Windows 8?

To disable recently access files disable it through the "Taskbar properties"

1. Go to search and lookup "taskbar". (Located in Settings)
2. Click on "Taskbar"
3. Uncheck "Store and display recently opened items in Jump Lists.

If you'd like to remove "Recent Places" you can simply right click it and remove it.

Does this help?

First, right click the Start Menu Orb / Button and click Properties.

Click Start Menu Tab (Or Jump Lists Tab for Windows 8) and uncheck the box Store and display recently opened items in the Start Menu and the taskbar. Click OK when done.

There is also the store recent documents and applications shortcuts Option in Taskbar Properties –> Jump Lists as explained here (might be the same thing)