Few organic molecules dissolve in water but why is this the case?
Pure water can form two hydrogen bonds per molecule. The enthalpy of these hydrogen bonds is about 23 kJ/mol of water. You have to give water a very good reason to rip apart its hydrogen bond network, and the interactions water experiences with the organic compounds often aren't enough, even considering increased entropy, to make this favorable.
Water is not a bad solvent for all organic molecules. In fact many organic molecules are soluble in water. In general the solubility of a substance in a given solvent is determined by the strength of the intermolecular forces between the solvent and solute.
The predominant intermolecular force in water is hydrogen bonding and so molecules with groups which can hydrogen bond generally dissolve well in water. These groups can have acidic hydrogens of their own such as alcohol or amine groups which can h-bond to water both through their hydrogens and through the lone pairs on their oxygen and nitrogen atoms respectively. Also other groups which have lone pairs on electronegative atoms such as carbonyl groups can h-bond with water and so will generally dissolve, although not as well as alcohols or amines. All of these groups are generally termed to be hydrophilic.
There are also hydrophobic groups which tend not to bond well with water and so do not tend to dissolve. These are generally groups which are non-polar and interact primarily through Van der Waals forces. Therefore they do not form strong interactions with water (because water primarily interacts through h-bonding) and so do not dissolve. These groups tend to be apolar, the most common example being alkyl groups.
So in answer to your question, many large organic molecules with predominant hydrophobic groups do not dissolve in water whereas smaller molecules with hydrophilic groups do tend to dissolve.
This questions has a more detailed discussion of the properties of water as a solvent: Why is water "the universal" solvent?