[Nexus 7 Q&A, Help & Troubleshooting] AndDiSa:
You need to adapt your udev-rules, i.e create a file named "51-android.rules" in /etc/udev/rules.d and put the following content into it, but replace the owner name by your login name:

# adb protocol on passion (Nexus One)
SUBSYSTEM=="usb", ATTR{idVendor}=="18d1", ATTR{idProduct}=="4e12", MODE="0600", OWNER="ds"
# fastboot protocol on passion (Nexus One)
SUBSYSTEM=="usb", ATTR{idVendor}=="0bb4", ATTR{idProduct}=="0fff", MODE="0600", OWNER="ds"
# adb protocol on crespo/crespo4g (Nexus S)
SUBSYSTEM=="usb", ATTR{idVendor}=="18d1", ATTR{idProduct}=="4e22", MODE="0600", OWNER="ds"
# fastboot protocol on crespo/crespo4g (Nexus S)
SUBSYSTEM=="usb", ATTR{idVendor}=="18d1", ATTR{idProduct}=="4e20", MODE="0600", OWNER="ds"
# adb protocol on stingray/wingray (Xoom)
SUBSYSTEM=="usb", ATTR{idVendor}=="22b8", ATTR{idProduct}=="70a9", MODE="0600", OWNER="ds"
# fastboot protocol on stingray/wingray (Xoom)
SUBSYSTEM=="usb", ATTR{idVendor}=="18d1", ATTR{idProduct}=="708c", MODE="0600", OWNER="ds"
# adb protocol on maguro/toro (Galaxy Nexus)
SUBSYSTEM=="usb", ATTR{idVendor}=="04e8", ATTR{idProduct}=="6860", MODE="0600", OWNER="ds"
# fastboot protocol on maguro/toro (Galaxy Nexus)
SUBSYSTEM=="usb", ATTR{idVendor}=="18d1", ATTR{idProduct}=="4e30", MODE="0600", OWNER="ds"
# adb protocol on panda (PandaBoard)
SUBSYSTEM=="usb", ATTR{idVendor}=="0451", ATTR{idProduct}=="d101", MODE="0600", OWNER="ds"
# adb protocol on panda (PandaBoard ES)
SUBSYSTEM=="usb", ATTR{idVendor}=="18d1", ATTR{idProduct}=="d002", MODE="0600", OWNER="ds"
# fastboot protocol on panda (PandaBoard)
SUBSYSTEM=="usb", ATTR{idVendor}=="0451", ATTR{idProduct}=="d022", MODE="0600", OWNER="ds"
# usbboot protocol on panda (PandaBoard)
SUBSYSTEM=="usb", ATTR{idVendor}=="0451", ATTR{idProduct}=="d00f", MODE="0600", OWNER="ds"
# usbboot protocol on panda (PandaBoard ES)
SUBSYSTEM=="usb", ATTR{idVendor}=="0451", ATTR{idProduct}=="d010", MODE="0600", OWNER="ds"
# adb protocol on grouper/tilapia (Nexus 7)
SUBSYSTEM=="usb", ATTR{idVendor}=="18d1", ATTR{idProduct}=="4e42", MODE="0600", OWNER="ds"
# fastboot protocol on grouper/tilapia (Nexus 7)
SUBSYSTEM=="usb", ATTR{idVendor}=="18d1", ATTR{idProduct}=="4e40", MODE="0600", OWNER="ds"
# adb protocol on manta (Nexus 10)
SUBSYSTEM=="usb", ATTR{idVendor}=="18d1", ATTR{idProduct}=="4ee2", MODE="0600", OWNER="ds"
# fastboot protocol on manta (Nexus 10)
SUBSYSTEM=="usb", ATTR{idVendor}=="18d1", ATTR{idProduct}=="4ee0", MODE="0600", OWNER="ds"

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# my own devices
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# Google Nexus 7 16 Gb Bootloader & recovery mode
SUBSYSTEM=="usb", ATTR{idVendor}=="18d1", ATTR{idProduct}=="4e40", MODE="0666", OWNER="ds" # Bootloader
SUBSYSTEM=="usb", ATTR{idVendor}=="18d1", ATTR{idProduct}=="d001", MODE="0666", OWNER="ds" # Recovery

# Google Nexus 7 16 Gb PTP mode (camera)
SUBSYSTEM=="usb", ATTR{idVendor}=="18d1", ATTR{idProduct}=="4e43", MODE="0666", OWNER="ds" # PTP media
SUBSYSTEM=="usb", ATTR{idVendor}=="18d1", ATTR{idProduct}=="4e44", MODE="0666", OWNER="ds" # PTP media with USB debug on

# Google Nexus 7 16 Gb MTP mode (multimedia device)
SUBSYSTEM=="usb", ATTR{idVendor}=="18d1", ATTR{idProduct}=="4e41", MODE="0666", OWNER="ds" # MTP media
SUBSYSTEM=="usb", ATTR{idVendor}=="18d1", ATTR{idProduct}=="4e42", MODE="0666", OWNER="ds" # MTP media with USB debug on

# Google Nexus 7 MTP mode : automatic unmount when unplugged
ENV{ID_MODEL}=="Nexus", ENV{ID_MODEL_ID}=="4e41", ACTION=="remove", RUN+="/usr/bin/fusermount -u /media/nexus7"
ENV{ID_MODEL}=="Nexus", ENV{ID_MODEL_ID}=="4e42", ACTION=="remove", RUN+="/usr/bin/fusermount -u /media/nexus7"