We present a theoretical analysis showing that layered topological insulators, for example, Bi$_2$Se$_3$ are optically hyperbolic materials in the range of terahertz (THz) frequencies. As such, these topological insulators possess deeply subdiffractional, highly directional collective modes$:$ hyperbolic phonon polaritons. We predict that in thin crystals the dispersion of these modes is split into discrete subbands and is strongly influenced by electron surface states. If the surface states are doped, then hybrid collective modes result from coupling of the phonon polaritons with surface plasmons. The strength of the hybridization can be controlled by an external gate that varies the chemical potential of the surface states. We also show that the momentum dependence of the plasmon-phonon coupling leads to a polaritonic analog of the Goos-Hänchen effect. The directionality of the polaritonic rays and their tunable Goos-Hänchen shift is observable via THz nanoimaging.