A three-dimensional eddy census data set was obtained from a global ocean simulation with one-tenth degree resolution and a duration of 7 years. The census includes 6.7 million eddies in daily data, which comprise 152,000 eddies tracked over their lifetimes, using a minimum lifetime cutoff of 28 days. Variables of interest include eddy diameter, thickness (vertical extent), minimum and maximum depth, location, rotational direction, lifetime, and translational speed. Distributions of these traits show a predominance of small, thin, short-lived, and slow eddies. Still, a significant number of eddies possess traits at the opposite extreme; thousands of eddies larger than 200 km in diameter appeared in daily data each year. A tracking algorithm found hundreds of eddies with lifetimes longer than 200 days. A third of the eddies are at least 1000 m tall and many penetrate the full depth of the water column. The Antarctic Circumpolar Current contains the thickest and highest density of eddies. Thick eddies are also common in the Gulf Stream, Kuroshio Current, and Agulhas ring pathway. The great majority of eddies extend all the way to the surface, confirming that eddy censuses from surface observations are a good proxy for the full-depth ocean. Correlations between variables show that larger-diameter eddies tend to be thicker and longer lived than small eddies.