Nexus 7 stuck in a boot loop
(EDIT)
This answer is only really helpful for unlocked tablets.. Look after this paragraph if that is already the case. Otherwise read on.  

"fastboot oem unlock" also does a factory reset, you need to have it unlocked before you need it, alas. This is both good for privacy and bad for recovery from half-bricked devices... The factory reset does In fact a secure erase which nullifies all your data.

According to Android: Building for devices:


  $ fastboot oem unlock
  The procedure must be confirmed on-screen, and deletes the user data for privacy reasons. It only needs to be run once.


$ fastboot boot recovery-clockwork-6.0.1.0-grouper.img 
downloading 'boot.img'...
FAILED (remote: Bootloader is locked.)
finished. total time: 0.020s
$ fastboot oem unlock
...
(bootloader) erasing userdata...
(bootloader) erasing userdata done
(bootloader) erasing cache...
(bootloader) erasing cache done
(bootloader) unlocking...
(bootloader) Bootloader is unlocked now.
OKAY [ 12.704s]
finished. total time: 12.704s
$ fastboot flash recovery recovery-clockwork-6.0.1.0-grouper.img 
sending 'recovery' (6480 KB)...
OKAY [  0.785s]
writing 'recovery'...
OKAY [  0.225s]
finished. total time: 1.010s
# after that boot into the recovery (don't boot normal! it overwrites valuable data...)
$ adb shell cat /dev/block/platform/sdhci-tegra.3/by-name/UDA \| gzip -1 -c \| uuencode bla | uudecode -o - | gunzip -dc | bar &gt; /media/qnap/backup/n7.data.formatted.img


(END EDIT)

You can boot a temporary custom recovery and create a backup of your device.

It should also be possible to wipe it afterwards and recover from your problem without having to send it back at all (provided it's not a hardware issue).

Steps:


install the SDK (if not already done) and have working adb + fastboot executables ready
Download a CWM recovery image from here
unlock your Nexus 7's bootloader: fastboot oem unlock
Here's how to enter the fastboot mode (the Nexus 7's codename is grouper):
Press Power for a second, and press Volume Down when the bootloader logo appears
boot into a temporary CWM recovery: fastboot boot recovery-clockwork-6.0.1.0-grouper.img
Create a nandroid/CWM backup from your broken installation (backup&amp;restore->backup)

after the backup is complete, try to pull all data from your device:
adb shell mount (should list something like /dev/block/mmcblk0p1 on /sdcard or so (not really sure however)
adb pull /sdcard backup/ (replace /sdcard with the above noticed directory, this should extract all your data to backup/)
check if everything is transmitted correctly)
you can buy TitaniumBackup+ProKey afterwards (it allows extracting data from Nandroid backups quite easily)

If that fails you can alternatively leech everything manually with adb:
I assume you use Linux.  


.  

#list available devices:
adb shell ls /dev/block
adb shell cat /proc/partitions
#create images for each mtdblock 
#uuencoding is needed because the shell interferes with the stream (adds linefeeds or so):
adb shell cat /dev/block/mtdblockX \| uuencode foo | uudecode -o mtdblockX.img
adb shell cat /dev/block/mmcblkXXX \| uuencode foo | uudecode -o mmcblkXXX
#compare md5sums:
adb shell md5sum /dev/block/*
md5sum mtdblock* mmcblk*

# Look for reasonably sized images and what file system they are:
ls -lh mtdblock* mmcblk*
file mtdblock* mmcblk*
# You should be able to mount those images now (if you happen to use linux):
mount -t ext4 -oloop,ro mtdblockX /media/mtdblockX
# Now use some file-explorer to access your saved data



Final step:
If you are really sure that you got all your data back, boot back into the CWM recovery (see step above) and issue a wipe data/factory reset command. Then reboot and re-setup your tablet (hopefully you don't have a hardware issue).  
Optional step: relock your bootloader via fastboot oem lock