Are there any organic compounds that do NOT contain hydrogen ? And if so, what are they?
Distinguishing organic and inorganic substances is often very formal. We say CX4 are organic compounds, we should also say carbon does not form carbon halogenides, which are inorganic compounds.



One of more known halogen-hydrogen-free examples is carbon suboxide $\ce{C3O2}$,  $\ce{O=C=C=C=O}$, that is somehere on inorganic-organic border, being often considered as the second anhydride of malonic acide $\ce{HOOC-CH2-COOH}$, as it is prepared from it by $\ce{P4O10}$ aggressive dehydratation. 

But the true malonic anhydride has 4-atom cycle.



One of less known examples is the anhydride of the mellitic acid, which could be formally considered as a carbon oxide with the summary formula $\ce{C12O9}$ 


  ... [mellitic anhydride] is one of the only four [oxides] that are reasonably stable under standard conditions.  It is a white sublimable solid, apparently obtained by Justus Liebig and Friedrich Wöhler in 1830 in their study of Mellite




As an interesting side info:


  Mellite, also called honeystone, is an unusual mineral being also an organic chemical.   Chemically identified as an aluminium salt of mellitic acid; that is, aluminium benzene hexacarboxylate hydrate, with the chemical formula $\ce{Al2C6(COO)6 \cdot 16H2O}$