Genome-wide association studies have helped us identify thousands of common variants associated with several widespread complex diseases. However, for most traits, these variants account for only a small fraction of phenotypic variance or heritability. Next-generation sequencing technologies are being used to identify additional rare variants hypothesized to have higher effect sizes than the already identified common variants, and to contribute significantly to the fraction of heritability that is still unexplained. Several pooling strategies have been proposed to test the joint association of multiple rare variants, because testing them individually may not be optimal. Within a gene or genomic region, if there are both rare and common variants, testing their joint association may be desirable to determine their synergistic effects. We propose new methods to test the joint association of several rare and common variants with binary and quantitative traits. Our association test for quantitative traits is based on genotypic and phenotypic measures of similarity between pairs of individuals. For the binary trait or case-control samples, we recently proposed an association test based on the genotypic similarity between individuals. Here, we develop a modified version of this test for rare variants. Our tests can be used for samples taken from multiple subpopulations. The power of our test statistics for case-control samples and quantitative traits was evaluated using the GAW17 simulated data sets. Type I error rates for the proposed tests are well controlled. Our tests are able to identify some of the important causal genes in the GAW17 simulated data sets.