What solutions are available for using iPad as an extended desktop? Occasionally, I would like to use my iPad (3rd gen, iOS7) as a second screen (an extension, NOT a mirror) for my Macbook Pro (Mountain Lion).

Is this possible without paying for an app in iOS7? Does Mavericks or iOS7 include any new related functionality? I am aware that there have been improvements for second displays in Mavericks.

See also: How to use the new iPad (3rd gen) as a second screen? and Is it possible to use an iPad as an additional computer monitor?
You will need an app to get this working properly, the nice new features in Mavericks are still essentially limited to traditionally connected displays via cables (DisplayPort/HDMI/Thunderbolt), rather than wireless connections.  There are many you can try, but my (unaffiliated merely personal preference) recommendation is Air Display.

Note that because the 2nd screen will be transferred over Wifi, you need to ensure that the iPad has a solid connection to the same LAN as your main Mac - being close to your Mac might be no good if they are both a distance away from the router...  As such, any usage of the iPad 2nd screen that requires fast refresh of window contents might not perform in any way like a proper monitor would, but it should be great for normal non video/gaming OS X apps.