You've probably heard by now about Adobe's AIR, a way to create "rich Internet applications" on the desktop. It's only for Windows and Mac at this point, but Adobe's plan is to eventually release it for Linux as well.
The idea is, on the face of it, another attempt to create a platform that lets you write an application once and run it anywhere. AIR applications can use generic HTML/Ajax, Adobe's Flash, or Flex, and Adobe wants AIR in as many places as possible -- multiple OS platforms, portable devices, you name it. That includes Linux by extension, and indeed Adobe is beginning some preliminary testing of AIR in Linux right now.
There's a few ways to think about how AIR could serve Linux. One is if it serves, in the long run, as a way to do rapid application development in Linux as well -- something like how (don't laugh) Visual Basic made it possible to do quick-and-dirty programming on Windows, and got many people hooked on programming for Windows in general. This I don't see happening without Adobe putting out a Linux IDE as well, or having someone refit an existing IDE like Eclipse to do the job.
Another possibility is that it will simply be a way to make Linux into a platform for whatever AIR applications get written -- making, in effect, Linux that much more natural a choice of platform next to Windows and the Mac for this kind of work. I suspect that will be the single biggest possibility, and maybe in some ways the best one: Linux will become yet another place for the same applications we see everywhere else, and that much easier a choice to adopt.