On a purely official basis, the only device that supposed to have Android 4.1 Jelly Bean is the newly announced Nexus 7 tablet, but it looks like the Samsung Galaxy Nexus smartphone can get some Jelly Bean action too.
This isn’t an official release from Google, but RootzWiki went ahead and made the Jelly Bean preview update available to the masses right after the Google I/O event. This update was originally intended for the GSM versions of the Galaxy Nexus, but it has been adapted to work with the LTE models too. This means that all Galaxy Nexus models are eligible for the Android 4.1 upgrade.
At this point, absolutely no bugs have been found and the ROM appears to be 100% functional. Of course, if you want to load up this somewhat unofficial version of Jelly Bean on your Galaxy Nexus, you will need to have root access. That said, if you want Google Now, offline voice dictation, and Project Butter speed, this is the only way you’ll get it at the moment.
You can get the “reverse engineered preview build” of Jelly Bean for your VZW Galaxy Nexus on Rootzwiki. Of course, proceed at your own risk.