Salts that are more hydrophilic than NaCl
As per DavePhD's answer, the contact angle of NaCl with water is zero, so we need another measure.

I think the word you are looking for is hygroscopic. http://en.wikipedia.org/wiki/Hygroscopy Substances which are so hygroscopic that they dissolve in the water they absorb from the atmosphere are said to be deliquescent, although the property of deliquesence in itself does not directly indicate the strength of a substance as a drying agent. 

The strength would best be measured as the equilibrium vapour pressure at a certain temperature, or alternatively, the temperature required to dehydrate: i.e. the temperature at which the vapour pressure of water vapour above the hydrated form of the substance becomes equal to atmospheric.

Cheap substances which are hygroscopic find applications as desiccants

Here is a list of some common ones http://en.wikipedia.org/wiki/List_of_desiccants. It includes the workhorse laboratory desiccants: silica gel for use in desiccators where products are dried under vacuum; molecular sieves, for drying solvents; CaCl2 for drying gases; and MgSO4 and CaSO4 in their anhydrous form for a quick drying of organic solutions. I would assume (though I'm not sure) that all of these would be stronger than NaCl. 

Unfortunately the really strong ones are missing, so here's a list of mine. The weaker ones above tend to act by physical absorption, or by changing from anhydrous crystals to hydrated crystals. Stronger ones tend to react chemically.

Concentrated sulfuric acid Strong enough to dehydrate sugar to "charcoal." One of the reasons for the affinity is the energy released when H2SO4 proponates H2O, forming HSO4- + H3O+. More of a curiousity than a desiccant. Not widely used as a desiccant because of its acidity. 

Phosphorous pentoxide Reacts with water to form various different polymeric phosphoric acids, ultimately ending up with 2P2O5 + 6H2O= 4H3PO4 though strength is gradually reduced as water is absorbed. Commonly used in the lab when a strong desiccant is required.

Calcium Oxide The reaction CaO + H2O = Ca(OH)2 has been proposed for large scale energy storage (the storage occurs in the reverse direction), but so far has been used only for smaller applications. As the calcium species are basic, exposure to air causes absorption of CO2, which then irreversibly degrades the material to bicarbonate and carbonate (unless heated to a much higher temperature.)  

Sodium Metallic sodium, extruded into wire using a press to increase its surface area, is the best way to ensure absolutely dry solvents.