We produce and analyse eclipse time variation (ETV) curves for some 2600 Kepler binaries. We find good to excellent evidence for a third body in 222 systems via either the light-travel-time (LTTE) or dynamical effect delays. Approximately half of these systems have been discussed in previous work, while the rest are newly reported here. Via detailed analysis of the ETV curves using high-level analytic approximations, we are able to extract system masses and information about the three-dimensional characteristics of the triple for 62 systems which exhibit both LTTE and dynamical delays; for the remaining 160 systems, we give improved LTTE solutions. New techniques of pre-processing the flux time series are applied to eliminate false positive triples and to enhance the ETV curves. The set of triples with outer orbital periods shorter than ˜2000 d is now sufficiently numerous for meaningful statistical analysis. We find that (i) there is a peak near im ≃ 40° in the distribution of the triple versus inner binary mutual inclination angles that provides strong confirmation of the operation of Kozai-Lidov cycles with tidal friction; (ii) the median eccentricity of the third-body orbits is e2 = 0.35; (iii) there is a deficit of triple systems with binary periods ≲1 d and outer periods between ˜50 and 200 d which might help guide the refinement of theories of the formation and evolution of close binaries; and (iv) the substantial fraction of Kepler binaries which have third-body companions is consistent with a very large fraction of all binaries being part of triples.