What solvent would have the fewest ions? We know that water auto-ionizes (to a rather small extent). 

My question is which solvent would have the fewest ions (or at least fewer ions than water). 

I'm thinking that perhaps some kind of hydrocarbon, as these are both weaker acids and weaker bases than water and thus even less reactive. I've seen computers submerged in oils (as well as distilled water) due to their low conductivities.
2-Methylpropane has a $\mathrm{p}K_\mathrm{a}$ of 53 ($\mathrm{p}K_\mathrm{a}$ table).  That sounds pretty non-ionic.  Can't think of any common all-carbon (no substituents of any kind) liquid compounds.