UPDATE: Both generations of the Nexus 7 (2012 and 2013) work with Plugable USB Ethernet adapters if they have been upgraded to the current Android version (5.1 as of this writing).
The new 2013 Google Nexus 7 (“Gen 2” or “flo”) has a bug where USB Ethernet adapters won’t work — they’ll appear to be recognized, but won’t get a DHCP address.
This is with Android 4.3, builds JSS15J and JSS15Q at least.
There is an open bug on this issue, we we’re hopeful that Google will fix quickly with an update:
https://code.google.com/p/android/issues/detail?id=58868
Until then, it’s important to realize that USB Ethernet adapters won’t work. So far, there is no evidence of this affecting other devices (e.g. the original Nexus 7 is not yet affected).
In combination with a USB OTG cable, it’s common to use USB Ethernet adapters to get wired network connectivity for performance (2-3x wireless) and security reasons.
For advanced users familiar with rooting devices and flashing custom ROMS, the latest CyanogenMod builds should now have this fixed.