Photo blogger Helen Bradley recently found herself in that situation, and details the steps she went through to get access to the Flash player on a 64-bit Windows 7 system. Essentially, the fix involves ensuring you're running the 32-bit version of Internet Explorer, and then backgrading to an older version of Flash; hit the post for the full details.
It's a workable fix, but one that shouldn't be necessary. We'd certainly endorse Bradley's conclusion:
Given that so many people are switching to 64-bit operating systems, if only because it allows you to address great wads of memory, it really is time that the big name companies came to the party and provided basic tools compatible with these systems.