Apple - How can I mount an ext4 file system on OS X?

The answer depends on you willingness to invest in commercial software:

If you don’t mind spending some money on a commercial product, Paragon’s extFS for Mac will give you read and write access to ext2 / ext3 / ext4 file systems. The current version supports all versions of OS X / macOS from 10.10 upwards.

If you are looking for a free solution, you can setup a Linux virtual machine, mount your volume(s) there and share it / them via Samba or (S)FTP. This post has some details on how to achieve this using VirtualBox, a free virtual machine application. Note this is not exactly a lightweight solution, even if using a prebuilt VirtualBox VM will spare you installing and configuring a Linux distro from scratch.

Building on Ken's answer: I used fuse4x and fuse-ext2 successfully, and I recommend fuse-ext2 over ext4fuse. fuse-ext2 provides write access while ext4fuse provides only read access. Note that despite its name, fuse-ext2 supports EXT2/EXT3/EXT4.

ext4fuse was a hassle for me, because it requires manual compilation and has no support for fuse4x options that would allow me to set access control. fuse-ext2 provides downloadable packages, and the 0.0.7 version worked just fine. I copied a few large ISOs over without any problem.

One can also install OSXFUSE completely via the brew command line package manager:

brew install homebrew/fuse/ext4fuse

Note that the installation tells certain commands need to be run as 'sudo' in addition to this.

With Yosemite better have a look at this. And then make sure the directory is readable by your user by doing this. For it to work I had to use the wheel group like this:

sudo dscl . append /Groups/wheel GroupMembership $(whoami)