Titanium dioxide (titania, TiO$2$) is a widely studied material with diverse applications. Here, we explore how pairwise and many-body descriptions of van der Waals dispersion interactions perform in atomistic modeling of the two most important TiO$2$ polymorphs, rutile and anatase. In particular, we obtain an excellent description of both bulk structures from density-functional theory (DFT) computations with the many-body dispersion (MBD) method of Tkatchenko and co-workers coupled to an iterative Hirshfeld partitioning scheme ("Hirshfeld-I"). Beyond the bulk, we investigate the most important crystal surfaces, namely, rutile (110), (101), and (100) and anatase (101), (100), and (001). Dispersion has a highly anisotropic effect on the different ($hkl$) surfaces; this directly changes the predicted nanocrystal morphology as determined from Wulff constructions. The periodic DFT+MBD method combined with Hirshfeld-I partitioning appears to be promising for future large-scale atomistic studies of this technologically important material.