You're not alone. Microsoft is aware of the issue and they are working to fix it. Zune service status from their website:
Customers with 30gb Zune devices may experience issues when booting their Zune hardware. We’re aware of the problem and are working to correct it. Sorry for the inconvenience, and thanks for your patience!
I'll post an update when one becomes available.
UPDATE: Instructions from Microsoft on a fix:
My Zune 30 is frozen on the boot screen, now what do I do?
You will need to reboot your device after noon GMT on Jan 1, 2009.
Please unplug your Zune (no AC or USB cables).
Because your Zune is frozen your device battery will begin draining, this is good.
The battery will eventually be fully depleted and the screen will go black.
After noon GMT on January 1 (that's 7 a.m. Eastern or 4 a.m. Pacific time) connect your AC power or USB cable such that the battery can begin charging again.
Once the Zune has enough battery to boot it should do so normally and you can go back to enjoying your Zune!
My Zune 30 has been working fine today, should I be worried?
Nope, your device is fine and will continue to work as long as you do not plug it into the PC before tomorrow.
If you plug your device into a PC before noon GMT Jan 1, 2009 your device clock will be set to the last day of the leap year and you will experience the freeze issue. If this happens, see above.
The PC that you plug into does not have to have the Zune software installed in order for your device clock to be set and the leap year bug to occur so you should avoid plugging your Zune 30 into any PC today.
What if I have DRM content on my Zune?
Your DRM content will most likely not be affected by this issue. However, it is a good idea to sync your device with your PC once the freeze has been resolved in order to ensure that all of your licenses are up to date.
What if I took the advice on the forums and hard reset my device by disconnecting the battery?
This is not a good idea and we do not recommend opening your device up yourself. However, if you already did it…
If you have DRM content on your device, your DRM store is now out of sync with your secure clock.
You will need to wait 24 hours from the time that you reset the device and then resync your DRM licenses from your PC.
Alternatively you can format your device and resync the content.
Told you I wouldn't recommend removing the battery :) Hopefully this will get everyone back up and working.