Ionic compound having highest solubility in water
Caesium salts are unapologetically ionic, and they typically have quite high mass solubilities in many solvents, including water.

Assuming organic ions are allowed, caesium acetate ($\ce{H3CCO2^-Cs+}$) in particular has a remarkably high solubility of 9451 g/kg water at −2.5 °C, increasing to 13 455 g/L water at 88.5 °C.

Caesium formate ($\ce{HCO2^-Cs+}$) is also quite soluble, with a solubility of 4880 g/kg water at 20 °C, resulting in 2.56 L of solution with a density of 2.297 g/mL (reference, .docx file). However, its solubility increases much faster with increasing temperature (J. Chem. Soc., Trans., 1922, 121, 1837-1843). At 100 °C, it reaches an outstanding value of 20 071 g/kg water! That's 11.6 molal, or roughly 20-25 mol/L assuming the density doesn't change too much. This saturated solution is 67.7% cesium formate by number of moles, which means more than two caesium ions and two formate ions per molecule of water.

I believe I have read somewhere that caesium formate is the record holder for highest mass solubility in water (evidently only at high temperatures). If this is not true, then I can scarcely believe it will be topped by much.

Tangentially, Ivan mentions Clerici's solution, which is actually a mixture of thallium(I) formate and thallium(I) malonate. The mixture doesn't count (though the individual components are quite soluble themselves), but it interesting to analyse. Apparently 300 g of each compound will dissolve in 40 g of water without saturating it room temperature (ref), giving a lower bound to their combined solubility of 15 000 g/kg water. This value rises with heating, and is the only way I can see to beat the mass solubility of caesium formate.

For further entertainment, I recommend these two solubility tables with a large number of entries (1, 2). The second one can be ordered by solubility at different temperatures. It's interesting to see the variety of cations and anions which can be combined to display extreme mass solubility.

Edit: If room-temperature ionic liquids are allowed, then it is quite likely some of them are miscible with water in any proportion, which is effectively "infinite solubility in water". Something as simple as ethylammonium nitrate ($\ce{C2H5NH3+NO3-}$) may suffice.