We summarize the occurrence of interplanetary coronal mass ejections (ICMEs) in the near-Earth solar wind during 1996--2002, corresponding to the increasing and maximum phases of solar cycle 23. In particular, we give a detailed list of such events. This list, based on in situ observations, is not confined to subsets of ICMEs, such as magnetic clouds or those preceded by halo coronal mass injections (CMEs) observed by the Solar and Heliospheric Observatory/Large Angle and Spectrometric Coronagraph, and provides an overview of 214 ICMEs in the near-Earth solar wind during this period. The ICME rate increases by about an order of magnitude from solar minimum to solar maximum (when the rate is ~3 ICMEs per solar rotation period). The rate also shows a temporary reduction during 1999 and another brief, deeper reduction in late 2000 to early 2001, which only approximately track variations in the solar 10-cm flux. In addition, there are occasional periods of several rotations duration when the ICME rate is enhanced in association with high solar activity levels. We find an indication of a periodic variation in the ICME rate, with a prominent period of ~165 days similar to that previously reported in various solar phenomena. It is found that the fraction of ICMEs that are magnetic clouds has a solar cycle variation, the fraction being larger near solar minimum. For the subset of events that we could associate with a CME at the Sun the transit speeds from the Sun to the Earth were highest after solar maximum.