We study several different kinds of bound states built from D-branes and orientifolds. These states are to atoms what branonium - the bound state of a brane and its anti-brane - is to positronium, inasmuch as they typically involve a light brane bound to a much heavier object with conserved charges which forbid the system's decay. We find the fully relativistic motion of a probe Dp′l-brane in the presence of source Dp-branes is integrable by quadratures. Keplerian conic sections are obtained for special choices for p and p′ and the systems are shown to be equivalent to non-relativistic systems. Their quantum behaviour is also equivalent to the corresponding non-relativistic limit. In particular the p = 6, p′ = 0 case is equivalent to a non-relativistic dyon in a magnetic monopole background, with trajectories in the surface of a cone. We also show that the motion of probe branes about D6-branes in IIA theory is equivalent to the motion of the corresponding probes in the uplift to M theory in 11 dimensions, for which there are no D6-branes but their fields are replaced by a particular Taub-NUT geometry. We further discuss the interactions of D-branes and orientifold planes having the same dimension. This system behaves at large distances as a brane-brane system but at shorter distances it does not have the tachyon instability. © SISSA/ISAS 2004.