According to Wikipedia, one of the last major hurdles in the isolation of elemental fluorine was the need to mix hydrogen fluoride with another substance in order for its electrolysis to be possible (Henri Moissan eventually hit upon potassium bifluoride, which is still used for this purpose today).
From "Fluorine Isolation":
Edmond Frémy postulated that electrolysis of pure hydrogen fluoride to generate fluorine was feasible and devised a method to produce anhydrous samples from acidified potassium bifluoride; instead, he discovered that the resulting (dry) hydrogen fluoride did not conduct electricity.
And from "Henri Moissan Preparation of elemental fluorine":
Moissan eventually succeeded in preparing fluorine in 1886 by the electrolysis of a solution of potassium hydrogen difluoride ($\ce{KHF2}$) in liquid hydrogen fluoride ($\ce{HF}$). The mixture was needed because hydrogen fluoride is a nonconductor.
However, hydrogen fluoride is a protic solvent, and undergoes autoionisation via the following reaction:
$$\ce{3 HF <=> H2F^+ + HF2^-}$$
Pure liquid $\ce{HF}$ should, therefore, conduct electricity at least weakly, like liquid water does.
What gives?