Large whole-genome sequencing projects have provided access to much of the rare variation in human populations, which is highly informative about population structure and recent demography. Here, we show how the age of rare variants can be estimated from patterns of haplotype sharing and how these ages can be related to historical relationships between populations. We investigate the distribution of the age of variants occurring exactly twice (f2 variants) in a worldwide sample sequenced by the 1000 Genomes Project, revealing enormous variation across populations. The median age of haplotypes carrying f2 variants is 50 to 160 generations across populations within Europe or Asia, and 170 to 320 generations within Africa. Haplotypes shared between continents are much older with median ages for haplotypes shared between Europe and Asia ranging from 320 to 670 generations. The distribution of the ages of f2 haplotypes is informative about their demography, revealing recent bottlenecks, ancient splits, and more modern connections between populations. We see the signature of selection in the observation that functional variants are significantly younger than nonfunctional variants of the same frequency. This approach is relatively insensitive to mutation rate and complements other nonparametric methods for demographic inference.