Adobe has released a beta of AIR for Linux. Good news, everyone with a 64-bit processor, or PPC, or Sparc, or ARM, or anything more exotic than 32-bit x86. AIR for Linux Release Notes say that all you need is:
Processor - Modern processor (800MHz or faster)
Finally, web applications have freed us from the tyranny of worrying about such difficult issues as endianness, alignment, and struct padding!

I have to admit. That is a bit sloppy from Adobe.
Either i am missing a joke, or it actually says:
"Processor - Modern x86 processor (800MHz or faster, 32-bit)"
Note the x86 part and the 32-bit part.
@Amir E. Aharoni
The page was edited today to add the x86 and 32-bit parts. You can still see the previous version that chromatic is commenting on.
Well, it's not like they're losing a lot of users in the world of Sparc desktops. Expensive _and_ slow - what a combination!
But the x64 thing, yeah, that's lame. I wonder what the issue is?
@Daniel, if it's anything like the Flash plugin for GNU/Linux, there's only one developer, and he's awfully busy just trying to get the code to compile, much less worry about 64-bit portability.