We present a statistical analysis of solar coronal mass ejections (CMEs) based on 23 years of quasi-continuous observations with the LASCO coronagraph, thus covering two complete Solar Cycles (23 and 24). We make use of five catalogs, one manual (CDAW) and four automated (ARTEMIS, CACTus, SEEDS, and CORIMP), to characterize the temporal evolutions and distributions of their properties: occurrence and mass rates, waiting times, periodicities, angular width, latitude, speed, acceleration and kinetic energy. Our analysis points to inevitable discrepancies between catalogs due to the complex nature of CMEs and to the different techniques implemented to detect them, but also to large areas of convergence that are critically important to ascertain the reliability of the results. The temporal variations of these properties are compared to four indices/proxies of solar activity: the radio flux at 10.7 cm (F10.7), the international sunspot number (SSN), the sunspot area (SSA), and the total magnetic field (TMF), either globally or separately in the northern and southern hemispheres in the case of the last three. We investigate the association of CMEs with flares, erupting prominences, active regions and streamers. We find that the CME occurrence and mass rates globally track the indices/proxies of solar activity with no time lag, prominently the radio flux F10.7, but the linear relationships were different during the two solar cycles, implying that the CME rates were relatively larger during SC 24 than during SC 23. However, there exists a pronounced divergence of the CME rates in the northern hemisphere during SC 24 as these rates were substantially larger than predicted by the temporal variation of the sunspot number. The distribution of kinetic energy follows a log-normal law and that of angular width follows an exponential law implying that they are random and independent. The distribution of waiting time (WTD) has a long power-law tail extending from 3 to 100 hr with a power-law index which varies with the solar cycle, thus reflecting the temporal variability of the process of CME formation. There is very limited evidence for periodicities in the occurrence and mass rates of CMEs, a striking feature being the dichotomy between the two hemispheres. Rather weak correlations are present among the various CME parameters and particularly none between speed and acceleration. The association of CMEs with flares and erupting prominences involves only a few percents of the overall population of CMEs but the associated CMEs have distinctly larger mass, speed, kinetic energy and angular width. A more pronounced association is found with active regions but the overwhelming one is with streamers further confirmed by the similarity between the heliolatitudinal distribution of CMEs and that of the electron density reconstructed from time-dependent tomographic inversion. We find no evidence of bimodality in the distributions of physical parameters that would support the existence of two classes, particularly that based on speed and acceleration, the distributions thus favoring a continuum of properties. There exists an excess of narrows CMEs which however does not define a special class. These narrow CMEs are likely associated with the ubiquitous mini-filaments eruptions and with mini flux ropes originating from small magnetic bipoles, the disruption mechanisms being similar to those launching larger CMEs. This supports the concept that CMEs at large arise from closed-field coronal regions at both large and small scales.