Can the iPad / iPad 2 handle iOS 6?
The short version:


Original iPad, no.
iPad 2, yes.


The details also matter for some features, per http://www.apple.com/ios/whats-new/#compatible:



There's also the device specific features fine print:


Turn-by-turn navigation is available only on iPhone 4S, iPhone 5, and iPad 2 or later with cellular data capability. Flyover is available only on iPhone 4S, iPhone 5, iPad 2 or later, and iPod touch (5th generation).
Siri is available on iPhone 4S, iPhone 5, iPad (3rd generation), and iPod touch (5th generation) and requires Internet access.
FaceTime video calling requires a FaceTime-enabled device for the caller and recipient and a Wi-Fi connection. FaceTime over a cellular network requires iPhone 4S, iPhone 5, or iPad (3rd generation) with cellular data capability.
Offline Reading List is available on iPhone 4 or later and iPad 2 or later.
Made for iPhone hearing aids require iPhone 4S or iPhone 5.
Panorama is available on iPhone 4S, iPhone 5, and iPod touch (5th generation).