Want to know the reason I am such a fan of Crossover? A few weekends ago I spent about 6 hours trying to get Wine sources to compile with various patches to make the Diablo 3 open beta work on Linux. The result? I ended up hanging my head in defeat and just playing on my OSx86 system so I didn't miss the weekend event. At that point Diablo 3 didn't work OOTB on default Wine builds or Crossover.
This morning I dropped by #crossover on FreeNode to check in with the Crossover folks to see what their plans were for the Diablo 3 release due out tonight - were us Linux folks going to have to wait?
Trouble Shooting Tips:
If you are having issues getting it to run via the latest Wine builds it might be worth your while to use winetricks to install the "vcrun2008" package.
If your login attempt is hanging at the "authenticating credentials" step, exit Diablo, open a terminal and run: