What are you pasting from Illy? That's pretty much limited to simple
shapes and objects.
As an update, just checked on a colleagues computer who is also on CS6 and a PC and he had no problem copying and pasting the above object, so might be a bug with my software?
You might want to check the prefs in Illy and see what you are putting on the clipboard.
Fixed it! Compared the CS5.5 and CS6 default settings on the clipboard like you suggested and found the discrepancies.
For anyone else having this issue going forward, instructions are below.
To be able to paste from InDesign into Illustrator, have your clipboard preferences as follows
To paste from Illustrator into InDesign, make sure you have these settings on your AI clipboard preferences