On the new HTC One M8 you can easily view the list of recent apps with the option to clear the list or re-open applications from the list of recent open apps.
To clear/view recent apps on HTC One M8, do as follows:
1. Turn the screen on and unlock your phone
2. Touch the Option key (the touch button right to the Home button) and the list of recent apps is opened
3. To clear all the applications in the list, touch the cross icon on the top right
4. To clear a specific app from the list, hold your finger on the app and swipe up