Recover from bootloop w/o erasing data?

This morning my phone decided not to boot anymore, but to go into a bootloop instead. The system is totally stock, no unlocked bootloader, no custom rom, nothing. Also, no OTA update was involved. Frankly, I know nothing about Android, so I appreciate all help I can get. I can't even remember which Android version it was running on (but I'm guessing it was JB). Before not booting anymore, I got various error messages from crashed apps and services, and I rebooted it manually.

Is there a way which I can try to recover from this without erasing all my data?

By now I figured out how to get into fastboot and talk to my phone from my computer (fastboot, not adb).
TIA Sebastian