We report an extensive investigation of the electric dipole moment (mu(alpha)), static polarizability (alpha(alpha beta)), and hyperpolarizability (beta(alpha beta gamma) and gamma(alpha beta gamma delta)) of the water dimer. Calculations were performed at both rigid and relaxed monomer geometries. At the rigid monomer geometry (RIMG), a very large [9s6p6d4f/6s5p3d2 f] basis set consisting of 370 Gaussian-type functions is thought to provide self-consistent field (SCF) values very close to the Hartree-Fock limit for all properties: total dipole moment mu=1.0706ea(0), mean and anisotropy of the dipole polarizability <(alpha)over bar> = 16.98 and Delta alpha=2.69e(2)a(0)(2)E(h)(-1), first hyperpolarizability (in the direction of the dipole moment vector) <(beta)over bar>=-2.9e(3)a(0)(3)E(h)(-2), and mean second dipole hyperpolarizability <(gamma)over bar>=1906e(4)a(0)(4)E(h)(-3). Very large electron correlation effects are observed for the hyperpolarizability. At the CCSD(T) level, coupled-cluster theory with single, double and perturbatively linked triple excitations, our best values are mu=1.0204ea(0), <(alpha)over bar>=19.54, and Delta alpha=3.06e(2)a(0)(2)E(h)(-1), <(beta)over bar>=-6.5e(3)a(0)(3)E(h)(-2), and <(gamma)over bar>=3669e(4)a(0)(4)E(h)(-3). <(alpha)over bar>((H2O)(2)) and <(gamma)over bar>((H2O)(2)) are not drastically different than twice the size of <(alpha)over bar>(H2O) and <(gamma)over bar>(H2O). Our efforts to estimate the interaction properties of two water molecules in the dimer lead to the conclusion that <(alpha)over bar>(inter) and <(gamma)over bar>(inter) are rather small. Further calculations at a relaxed monomer geometry (REMG) corroborate this conclusion. We have fully explored basis set effects at all levels of theory and for all properties. We rely on a sequence of small-sized but sufficiently flexible basis sets in order to propose reliable computational strategies for the extension of electric property calculations to large water clusters.