Using observations from the High Energy Telescopes (HETs) on the STEREO A and B spacecraft and similar observations from near-Earth spacecraft, we summarize the properties of more than 200 individual > 25 MeV solar proton events, some detected by multiple spacecraft, that occurred from the beginning of the STEREO mission in October 2006 to December 2013, and provide a catalog of these events and their solar sources and associations. Longitudinal dependencies of the electron and proton peak intensities and delays to onset and peak intensity relative to the solar event have been examined for 25 three-spacecraft particle events. Expressed as Gaussians, peak intensities fall off with longitude with σ=47±14∘ for 0.7 – 4 MeV electrons, and σ=43±13∘ for 14 – 24 MeV protons. Several particle events are discussed in more detail, including one on 3 November 2011, in which ∼ 25 MeV protons filled the inner heliosphere within 90 minutes of the solar event, and another on 7 March 2012, in which we demonstrate that the first of two coronal mass ejections that erupted from an active region within ∼ 1 hour was associated with particle acceleration. Comparing the current Solar Cycle 24 with the previous cycle, the first > 25 MeV proton event was detected at Earth in the current solar cycle around one year after smoothed sunspot minimum, compared with a delay of only two months in Cycle 23. Otherwise, solar energetic particle event occurrence rates were reasonably similar during the rising phases of Cycles 23 and 24. However, the rate declined in 2013, reflecting the decline in sunspot number since the peak in the northern-hemisphere sunspot number in November 2011. Observations in late 2013 suggest that the rate may be rising again in association with an increase in the southern sunspot number.