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We present the results of a speckle interferometric survey made with the CHARA speckle camera and 4 m–class telescopes of Galactic O-type stars with V < 8. We can detect with the speckle camera binaries in the angular separation range 0035 < ρ < 15 with Δm < 3, and we have discovered 15 binaries among 227 O-type systems. We combined our results on visual binaries with measurements of wider pairs from the Washington Double Star Catalog and fainter pairs from the Hipparcos Catalogue, and we made a literature survey of the spectroscopic binaries among the sample. We then investigated the overall binary frequency of the sample and the orbital characteristics of the known binaries. Binaries are common among O stars in clusters and associations (>59% have a visual or spectroscopic companion) but less so among field and especially runaway stars. There are many triple systems among the speckle binaries, and we discuss their possible role in the ejection of stars from clusters. The period distribution of the binaries is bimodal in log P, but we suggest that binaries with periods of years and decades may eventually be found to fill the gap. The mass ratio distribution of the visual binaries increases toward lower mass ratios, but low mass ratio companions are rare among close, spectroscopic binaries (probably because of the difficulty of spectroscopic detection rather than a real deficit). We present distributions of the eccentricity and longitude of periastron for spectroscopic binaries with elliptical orbits, and we find strong evidence of a bias in the longitude of periastron distribution (the "Barr effect"), which is probably caused by line distortions introduced by circumstellar gas.