We present energetic particle measurements from the Low-Energy Magnetospheric Measurement System (LEMMS) on board the Cassini spacecraft during its heliospheric cruise to Saturn. We cover 3 years (2000--2002) of data during the maximum of the solar cycle 23. Cassini's heliocentric radial distance ranged from 2.5 to 8.0 AU. Energetic particle intensity enhancements were associated with either sporadic intense solar energetic particle events, the effects produced by recurrent corotating interaction regions, or the arrival of transient interplanetary shocks. High-energy (>25 MeV) ion intensity enhancements were exclusively associated with the prompt component of intense solar energetic particle events. The largest low-energy (<1 MeV) ion and near-relativistic (43--305 keV) electron intensities occurred at the passage of interplanetary shocks. We compare particle intensities measured during the major solar energetic particle events near Earth with those measured at Cassini. We find that in general, the most intense events were observed by both Cassini and near-Earth spacecraft. However, the arrival of energetic particles at Cassini's larger heliocentric distance was modulated by the presence of magnetic field structures formed between the Sun and Cassini. We analyze the relative intensities of the particle events at Cassini in terms of the level of solar activity during the previous solar rotation. When a new injection of solar energetic particles occurs after a period of intense solar activity, it may produce a particle event at 1 AU but not at Cassini. Transient plasma flows generated by previous solar events can act as effective barriers to the propagation of energetic particles to Cassini. These structures cause delays in the expected arrival time of energetic particles at Cassini as well as an effective diminution of the prompt component of the solar energetic particle events at heliocentric distances from 2.5 to 8.0 AU.