Single-cell sequencing is emerging as a critical technology for understanding the biology of cancer, neurons, and other complex systems. Here we introduce Ginkgo, a web platform for the interactive analysis and quality assessment of single-cell copy-number alterations. Ginkgo fully automates the process of binning, normalizing, and segmenting mapped reads to infer copy number profiles of individual cells, as well as constructing phylogenetic trees of how those cells are related. We validate Ginkgo by reproducing the results of five major single-cell studies, and discuss how it addresses the wide array of biases that affect single-cell analysis. We also examine the data characteristics of three commonly used single-cell amplification techniques: MDA, MALBAC, and DOP-PCR/WGA4 through comparative analysis of 9 different single-cell datasets. We conclude that DOP-PCR provides the most uniform amplification, while MDA introduces substantial biases into the analysis. Furthermore, given the same level of coverage, our results indicate that data prepared using DOP-PCR can reliably call CNVs at higher resolution than data prepared using either MALBAC or MDA. Ginkgo is freely available at http://qb.cshl.edu/ginkgo.