Topologies of the electron intracule and extracule densities, I(R) and E(R), are analyzed. These topologies are found to be inherently more complex than those of the one-electron density. The main topological features of I(R) and E(R) are already present in the densities calculated within the Hartree-Fock (HF) approximation. Results of test calculations on several planar systems show that the positions and properties of attractors in I(R) and E(R) are predicted with a surprising fidelity by a naive independent-atom model, making it possible to index distinct types of electron pairs present in atoms and molecules. In general, each pair of atoms in a given molecule has the potential of producing a pair of attractors in I(R). At the HF level of theory, all the atoms collectively furnish a single attractor in I(R) at R=0, but this topological pattern is bound to change upon the inclusion of electron correlation. The attractors in E(R) stem from both individual atoms and atomic pairs. In addition, attractors that are not associated with either of these entities are observed. The plethora of attractors present in I(R) and E(R) give rise to complicated patterns of other critical points. Unusual. topological features, such as attractors linked by multiple interaction lines and bifurcations at bond points, are also encountered.