We present a statistical analysis of coronal mass ejections (CMEs) imaged by the Heliospheric Imager (HI) instruments on board NASA's twin-spacecraft STEREO mission between April 2007 and August 2017 for STEREO-A and between April 2007 and September 2014 for STEREO-B. The analysis exploits a catalogue that was generated within the FP7 HELCATS project. Here, we focus on the observational characteristics of CMEs imaged in the heliosphere by the inner (HI-1) cameras, while following papers will present analyses of CME propagation through the entire HI fields of view. More specifically, in this paper we present distributions of the basic observational parameters - namely occurrence frequency, central position angle (PA) and PA span - derived from nearly 2000 detections of CMEs in the heliosphere by HI-1 on STEREO-A or STEREO-B from the minimum between Solar Cycles 23 and 24 to the maximum of Cycle 24; STEREO-A analysis includes a further 158 CME detections from the descending phase of Cycle 24, by which time communication with STEREO-B had been lost. We compare heliospheric CME characteristics with properties of CMEs observed at coronal altitudes, and with sunspot number. As expected, heliospheric CME rates correlate with sunspot number, and are not inconsistent with coronal rates once instrumental factors/differences in cataloguing philosophy are considered. As well as being more abundant, heliospheric CMEs, like their coronal counterparts, tend to be wider during solar maximum. Our results confirm previous coronagraph analyses suggesting that CME launch sites do not simply migrate to higher latitudes with increasing solar activity. At solar minimum, CMEs tend to be launched from equatorial latitudes, while at maximum, CMEs appear to be launched over a much wider latitude range; this has implications for understanding the CME/solar source association. Our analysis provides some supporting evidence for the systematic dragging of CMEs to lower latitude as they propagate outwards.