Uncertainty about the demographic history of populations can hamper genome-wide scans for selection based on population genetic models. To obtain a portrait of the effects of demographic history on genome variability patterns in Drosophila melanogaster populations, we surveyed noncoding DNA polymorphism at 10 X-linked loci in large samples from three African and two non-African populations. All five populations show significant departures from expectations under the standard neutral model. We detect weak but significant differentiation between East (Kenya and Zimbabwe) and West/Central sub-Saharan (Gabon) African populations. A skew toward high-frequency-derived polymorphisms, elevated levels of linkage disequilibrium (LD) and significant heterogeneity in levels of polymorphism and divergence in the Gabon sample suggest that this population is further from mutation-drift equilibrium than the two Eastern African populations. Both non-African populations harbor significantly higher levels of LD, a large excess of high-frequency-derived mutations and extreme heterogeneity among loci in levels of polymorphism and divergence. Rejections of the neutral model in D. melanogaster populations using these and similar features have been interpreted as evidence for an important role for natural selection in shaping genome variability patterns. Based on simulations, we conclude that simple bottleneck models are sufficient to account for most, if not all, polymorphism features of both African and non-African populations. In contrast, we show that a steady-state recurrent hitchhiking model fails to account for several aspects of the data. Demographic departures from equilibrium expectations in both ancestral and derived populations thus represent a serious challenge to detecting positive selection in genome-wide scans using current methodologies.