Install a Camera Launcher
The Nexus 7 has a front-facing camera but there's no way to launch it from the homescreen out of the box. Install Camera Launcher by MoDaCo to be able to launch the device's camera straight from the homescreen.
Install Adobe Flash
Apple's iOS doesn't support Flash, but your brand new device does. While the Flash app is long gone from Google Play, you can still install it by downloading the APK from XDA developers (make sure to go to settings –> security first and check "unknown sources.")
Unlock Screen Rotation
A funny thing happened when Eric brought the Nexus 7 to AndroidPIT's offices for the first time: we couldn't initially figure out how to rotate the screen to landscape mode. Eric joked, "I feel like I just bought a giant phone." In fact, you can unlock screen rotation. Just pul down the notifcation bar and click the lock next to "Settings."
Transform Your Nexus 7 Into a Kindle eReader
Seriously, who needs a Kindle when you can download Amazon's Kindle app and sync your e-books to your Nexus 7? It's got by far the greatest number of books of any eReader app.
Play VLC Video Files
When you play MKV, AVI, or such video files, the stock video player will not work and MX player will only support S/W, S/W fast which blurs the video. Instead, try DicePlayer (you can get it from play store here). It supports H/W, which kills my nexus 7 battery a lot more quickly but plays video without over-pixelation.
Install Jelly Bean 4.1.1
Since you're now the proud owner of a certified Nexus device, you should see the option to upgrade to Android 4.1.1 Jelly Bean right out of the device. Do it. You won't be disappointed.
Use Streaming Music Apps
Because the storage space on the Nexus 7 is quite limited, I'd recommend using a streaming service like Google Music or Spotify. TuneIn Radio also works well. Unless you spring for a 16GB model, you're not going to have a lot of space to work with.
Don't Forget Your Freebies
Google doesn't advertise this nearly as much as they should, but your Nexus 7 comes with $20 credit – more than enough to download all the top tablet apps right out of the box. You'll be notified of your credit as soon as you open Google Play. Owners can also stream Transformers 3: Dark of the Moon for free (UPDATE: We just learned that Google no longer offers credit for new Nexus 7 owners).
(Top photo: TechCrunch.com)