The latest non-toxic solvent of choice is... Art Treehouse's Biobased Artist's Thinner.
This soy-based thinner doesn't really make the traditional oil paint 'glide' like Gamsol does, but hey I've been able to paint with my windows closed. No headache, no sore throat, no need to listen to Nick Cave or Leonard Cohen. Plus, it doesn't make the paint oily or glossy. The drying time doesn't change either. It's a bit more expensive than Gamsol but I'd be happy to pay extra!
(note: I use this thinner by itself to thin the paint for the initial layer of alla prima painting process & cleaning - probably not suitable for glazing, etc., or I have no idea how this will act with other mediums since I don't use any)