They will be relevant up to the point where operating systems simply makes their functionality a native element of their file system.
At least Drew is wise to the fact that they could become an also-ran, so it's not like this will happen to them overnight.
Someday they may all have Dropbox-like functionality built in, and someday after that they may interoperate. Dropbox can stay in their current business a long time regardless.
I run Windows and Debian on my desktops and laptop and I recently decided to try Ubuntu One. I could find no mention of other Linux OSes on the Ubuntu One page, and a quick web search returned nothing encouraging.
I was surprised by this. The impression I got is that Ubuntu One is just for people whose main OS is Ubuntu and who may have to also use Windows from time to time.
Anybody who was a mac user before 2000 can tell you how painful it was to use a mac when your friends or coworkers had windows. It was horrible. Problems with file sharing between systems created huge network effects for microsoft. It killed the possibility of having a mac for a lot of people.
The fundamental problem of compatibility requires not only technological and architectural commitment but also willingness to cooperate with competitors for the sake of the user.
But you're spot on with varying OSes being willing to cooperate to allow multiple clients access to shared data stores. Google, Apple, Microsoft and open source all in agreement on file sharing? Right.....
Surely the latest Dropbox investors considered that, and gauged the probability of harmony among the OS providers for the sake of the user. And since Dropbox just closed $250MM in financing, they obviously believe their chances are pretty good. :-)
At which point, they become a service. This is admittedly a wide-eyed optimist ideal, but I would picture most OS' adding basically a "Cloud storage" drive option that allows the user to mount any cloud storage service like a physical hard drive. The "driver" would be the interface protocol between the service and the user, and it would allow the various OS' to use the cloud storage as an additional, fully functional drive.
It probably won't happen until the next round of antitrust hearings against everyone(Apple, MS, Debian, Ubuntu, etc.), though...
Unfortunately Microsoft turned it in to something that didn't work anywhere near as well. It might have been improved now, but my business partner and I moved across to Dropbox, which has been much better. Since then I've also received files from various people working on joint projects across Dropbox, within the web industry it appears to have become the standard for that.
Getting something else that works well on one OS will be straightforward, especially for someone like Apple. Getting it to work well (and wanting it to) for multiple OSes and getting people on the other OSes to adopt it will be another matter.
That's partly why Dropbox survived their security problems so well, it's become part of a lot of people's background workflow.
Although Microsoft and Google have tried this sort of thing before (and a long time ago if we include WebDAV & Web folders) there is nothing quite like a successful product that gets it right and takes over to light a rocket underneath the bigger companies.
If iCloud takes off most Apple users won't look at Dropbox. Those of us already using it may find we use it less and if they then add a simple, cross-platform way to share files & folders we may just move on completely.
There's a lot of ifs there, but I believe that iCloud will at the least hamper Dropbox's move into the mainstream.