This variant of adbfs works even WITHOUT having root access (busybox) on your phone!

Instructions:

You will need libfuse-dev and adb. You will also need build-essential, git, and pkg-config. On Ubuntu:

sudo apt-get install libfuse-dev android-tools-adb
sudo apt-get install build-essential git pkg-config

Clone the repository:

git clone git@github.com:spion/adbfs-rootless.git
cd adbfs-rootless

Build:

make

Optional: If you have a separate copy of android-sdk and would like to use that adb, copy the binary adbfs to the android-sdk/platform-tools directory. If platform-tools is in your $PATH you can skip this step.

Create a mount point if needed (e.g. in your home directory):

mkdir ~/droid

You can now mount your device (also from the platform-tools dir):

./adbfs ~/droid

If you want to trigger a media rescan after every operation, use the option -o rescan:

./adbfs -o rescan ~/droid

Have fun!

Troubleshooting

Error: device not found

When running you get the following error:

--*-- exec_command: adb shell ls
error: device not found

Solution: Make sure that USB Debugging is enabled.

Then fusermount -u /media/mount/path before trying again. Note that if for any reason fusermount is not available in your system, you can use sudo umount /media/mount/path instead.

Error: device offline

When running you get the following error:

--*-- exec_command: adb shell ls
error: device offline

Solution: Make sure that

Your android-sdk-tools are up to date. Newer versions of Android also require newer versions of adb. For more info, see this Stack Overflow post.
You answer Yes when your phone asks whether it should allow the computer with the specified RSA key to access the device.

Then killall -9 adb; fusermount -u /media/mount/path before trying again.