We use molecular dynamics simulations to study attractive interactions and the underlying ionic correlations between parallel like-charged rods in the absence of additional salt. For a generic bulk system of rods we identify a reduction of short-range repulsions as the origin of a negative osmotic coefficient. The counterions show signs of a weak three-dimensional order in the attractive regime only once the rod-imposed charge inhomogeneities are divided out. We also treat the case of attraction between a single pair of rods for a few selected line charge densities and rod radii, Measurements of the individual contributions to the force between close rods are studied as a function of Bjerrum length. We find that even though the total force is always attractive at sufficiently high Bjerrum length, the electrostatic contribution can ultimately become repulsive. We also measure azimuthal and longitudinal correlation functions to answer the question how condensed ions are distributed with respect to each other and to the neighboring rod. For instance, we show that the prevalent image of mutually interlocked ions is qualitatively correct, even though modifications due to thermal fluctuations are usually strong.