What covalent compounds are soluble in water?
Water is a polar covalent compound. Alcohols are also polar covalent compounds.
According to solubility rules, "like solutes dissolves in like solvents"
This why water cannot dissolve oil, which is a nonpolar covalent compound.
There are many covalent or non-polar compounds that will dissolve in water like sugar, carbon dioxide gas, and many alcohols, but they do not break into ions the way ionic compounds do when they dissolve. They are basically pulled apart into smaller pieces of the same molecule. Usually if an organic or covalent compound is small, it is more likely to dissolve.
The covalent compounds that dissolve do so because they tend to have parts of their molecules that are somewhat polar (a negative side and a positive side) just like water.
The picture above shows sugar molecules dissolving in water. The sugar molecules contain polar O-H bonds. The polar O-H bonds in water attract the sugar molecules into solution.