It is indeed possible and in some ways is already done.
There's softer methods (like producing viruses). These retrieve data directly and mean that less computation power is needed by the hacker (an example being the AV coin project that launched from this site a while back).
There is then the "brute force" approach, which doesn't work as well with Bitcoin (as there's so many posibilities) and takes lots of time and computation due to the difficulty.