No ID and slow wi-fi
My experience on 2 trips between CPH and STO on X200 trains last week (Sept 2010) was that my ticket was checked, but my ID was never requested. From CPH I used a 2cl ticket purchased at the window. I reserved 1cl by phone for the return and printed at kiosk in STO.
The wi-fi was pathetically slow or spotty throughout both trips. As far as I can tell, there is no value in their free wifi, and it's certainly not worth paying for. My e-mail was unable to complete even a basic check, because the server kept timing out due to my slow connection.
Mobile phone service was fine throughout the journey, but I only used it for TXT.