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.