Recently, I've switched to cleaning my palette with walnut oil. This oil has been of use to painters for centuries, and is famously mentioned by Leonardo DaVinci as an oil painting medium.
Here I'm using walnut oil to clean my palette in the middle of a painting session. Whereas in the past I would use a solvent like turpentine, walnut oil does just as good of a job, and does not produce harmful vapors.
Above is the finished product- a clean palette ready to go!