Rockbox could rock the Zune open source-style
Okay, but the next question is usually whether you can install Linux.
Well, you can't really do either with the Microsoft Zune yet, but that doesn't mean you won't be able to upgrade (or downgrade) it by replacing the preinstalled software with some open-source firmware.
Rockbox is an open-source firmware replacement for MP3 players. Currently there are ports for a number of iRiver, Archos, and Apple iPod models. Work is underway to port Rockbox to the Toshiba Gigabeat F and X series. Microsoft's Zune is manufactured by Toshiba and has more in common with the Gigabeat S than the F or X series, but one of the main developers behind Rockbox says a Zune Port could be on the way. One of the main roadblocks would be the security features built into the Zune because of it's Wi-Fi capabilities.
Of course, installing Rockbox on a Zune would probably mean you couldn't play music purchased from the Zune Marketplace, and would definitely mean voiding your warranty. And odds are you wouldn't be able to share files with other Zune users via Wi-Fi (but who really does that anyway). On the other hand, this could be the first step towards using the Wi-Fi for something useful, like web browsing.
I wouldn't expect to see any major developments for a couple of months at least. The Toshiba porting is still underway, and as far as I can tell nobody's actively working on a Zune port just yet.