Water molecules are made of slightly positively charged hydrogen atoms and slightly negatively charged oxygen atoms. which force keeps water molecules stuck to one another?

In a chemical system, inter- and intra-molecular forces of interactions are operable. Intramolecular forces are the forces that hold atoms together within a molecule, while intermolecular forces are forces that exist between molecules. Thus, it is intermolecular forces of attraction which holds two or more molecules together.

intermolecular forces are of following types 
1) Dispersion
2) Dipole-Dipole interaction
3) Ion-Dipole Interaction and
4) Hydrogen bonding.

In case of water, it is Hydrogen bonding which is responsible for holding molecules together.

With reference to hydrogen bonding, it must be noted that it is an electrostatic attractive interaction between hydrogen atom that is bonded to 
electronegative atom (such as nitrogen, oxygen, or fluorine) and another atom, adjacent to it, which has lone pair of electrons.

In case of water, hydrogen atom of one water molecule interacts with lone pairs of electrons present on oxygen atom of other water molecule.