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In a recent series of papers we have developed and tested an algorithm for quantitatively measuring the topology of large-scale structure in the universe. We apply this algorithm to a large number of observational data sets. These include an Abell cluster sample out to V_max_ = 22,600 km s^-1^, the Giovanelli and Haynes sample out to V_max_ = 11,800 km s^-1^, the CfA sample out to V_max_ = 5000 km s^-1^, the Thuan and Schneider dwarf sample out to V_max_ = 3000 km s^-1^, and the Tully sample out to V_max_ = 3000 km s^-1^. When the topology is studied on smoothing scales significantly larger than the correlation length, we find that the topology is spongelike, in agreement with the random phase formula for the genus-threshold density relation, g_s_ is proportional to (1 - v^2^)e^-v^2^/2^. This is consistent with the standard model in which the structure we see in the universe today has grown from small fluctuations caused by random quantum noise in the early universe. When the smoothing length is λ ~ 600 km s^-1^, approximately equal to the galaxy correlation length, we see a small shift in the g_s_(v) curve in the direction of a "meatball" (isolated cluster) topology. When we analyze numerical simulations of a biased cold dark matter (CDM) universe, we find similar shifts, but not as large as those found in the observational data. A CDM or other hierarchical clustering model with stronger biasing or more nonlinear evolution might explain the observed shifts. Heavy neutrino models fit the observations less well than CDM models. We find no evidence for bubbles (i.e., voids surrounded on all sides by walls of galaxies) in these samples, although bubbles with diameters in the range 2500-4000 km s^-1^ across could have been detected if present. All asymmetries observed in the g_s_(v) curve are opposite to those expected for a bubble model. The CDM model gives a good fit to the observed amplitude of the genus curve as a function of the smoothing length, and, of the models studied, it is overall the most successful in explaining the data.