[Nexus 7 (2013) Q&A] sasuke12096:
This fixed it:

I haven't seen this on a Nexus 4 yet, but I had this happen last night on a Nexus 5 and got it fixed this evening. A call to T-mobile indicated that they haven't run across it yet either, but I found an XDA thread where they were seeing on a Galaxy S4. I'll post some steps for a somewhat tricky fix and then a write-up on what I think is happening based on what I found. Hopefully this will help.

1) Power off phone. Hold power button down until you see the Google logo come up and then disappear. That should stop the "boot loop" and keep the phone powered off. If it comes back on, try again and just hold the power button down a little longer than you thought you needed to.

2a) Steps 2-5 below can probably be replaced by putting the phone into airplane mode quickly while it's temporarily alive during the boot loop. If you put it into airplane mode and the boot loop stops, skip to step 6 and just disable airplane mode for steps 9/10.

2) Eject SIM card. You should have the little tool (round with a short, narrow point) that presses into a tiny hold on the side of the phone to eject the sim card. If you are uncertain on this step, get some help.

3) Power on phone. If you were connected to Wi-Fi when this started, it will still boot loop so we need to disable Wi-Fi as well. This is the tricky part. You may find it easy if you power off your wireless router before trying to turn off Wi-Fi on your phone.

4) Disable Wi-Fi as quickly as possible by swiping lock screen, pulling down the settings "drawer" at the top of the phone, clicking on wi-fi and click it off.

5) The phone should no longer reboot, but will start to reboot again if you give it a network connection (wi-fi or mobile) so don't reconnect it to the network until you are done with the next couple steps.

6) Go to Settings -> Apps and scroll over to ALL.

7) Scroll down to Google Services Framework and click it

8) Click on CLEAR DATA and hit Ok. I also hit CLEAR CACHE and while I'm not sure it's necessary, I recommend doing that as well.

9) Power off phone, re-install SIM card and power on phone.

10) Assuming you don't immediately go into a boot loop again, it's probably fixed. Re-enable wi-fi and go back to enjoying life :)

The trickiest part here is being fast enough to disable wi-fi before the reboot happens. It may be a non-issue if turning off the wireless router helps.

As a caveat, we haven't been running the phone for very long after clearing that data, but it's acting a little sluggish at times. I'm going to let it run for a day or two and then maybe do a full factory reset if it doesn't clear up. At the very least, the boot loop is gone.

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Now for the nerdy stuff in the hopes someone from the major providers and/or Google is watching this...

Late last night, I hooked up ADB to the phone after getting Wi-Fi disabled and USB Debugging enabled. A logcat dumped out a huge amount of data, but thankfully caught the reboot when I re-enabled Wi-Fi. Here's a partial dump from the log:

I/iu.SyncManager( 1201): NEXT; no task

I/CheckinRequestBuilder( 1201): Checkin reason type: 12 attempt count: 1

D/dalvikvm( 1087): GC_CONCURRENT freed 417K, 4% free 18384K/19056K, paused 2ms+2ms, total 19ms

W/dalvikvm( 744): threadid=13: thread exiting with uncaught exception (group=0x41564ba8)

E/AndroidRuntime( 744): *** FATAL EXCEPTION IN SYSTEM PROCESS: android.bg

E/AndroidRuntime( 744): java.lang.NullPointerException

E/AndroidRuntime( 744): at android.content.PeriodicSync.syncExtrasEquals(PeriodicSync.java:150)

E/AndroidRuntime( 744): at android.content.PeriodicSync.equals(PeriodicSync.java:129)

E/AndroidRuntime( 744): at com.android.server.content.SyncStorageEngine.setPeriodicSyncTime(SyncStorageEngine.java:1625)

E/AndroidRuntime( 744): at com.android.server.content.SyncManager$SyncHandler.scheduleReadyPeriodicSyncs(SyncManager.java:2097)

E/AndroidRuntime( 744): at com.android.server.content.SyncManager$SyncHandler.handleMessage(SyncManager.java:1881)

E/AndroidRuntime( 744): at android.os.Handler.dispatchMessage(Handler.java:102)

E/AndroidRuntime( 744): at android.os.Looper.loop(Looper.java:136)

E/AndroidRuntime( 744): at android.os.HandlerThread.run(HandlerThread.java:61)

I/Process ( 744): Sending signal. PID: 744 SIG: 9

I/ServiceManager( 176): service 'package' died

I/ServiceManager( 176): service 'batterystats' died

I/ServiceManager( 176): service 'usagestats' died

W/Sensors ( 1876): sensorservice died [0x7645fde0]

D/AndroidRuntime( 1087): Shutting down VM

many more services dieing

Note the null pointer exception in android.bg on a "PeriodSync" I don't know what that's supposed to do, but it clearly can only trigger with a valid network connection and it is very displeased with life. A search for some key words from the traceback led me to XDA (http://xdaforums.com/showpost.php?p=62943303&postcount=2119). The symptoms matched what I was seeing and they mention going into Airplane mode to stop the boot loop which may be an even better approach than my somewhat heavy handed solution above. Speculation in that thread indicates a google apps update of some sort which I assume probably came through on my wife's phone last night with automatic updates.