To better understand the quantitative characteristics and structure of phenotypic diversity, we measured over 14,000 transcript, protein, metabolite, and morphological traits in 22 genetically diverse strains of Saccharomyces cerevisiae. More than 50% of all measured traits varied significantly across strains [false discovery rate (FDR) = 5%]. The structure of phenotypic correlations is complex, with 85% of all traits significantly correlated with at least one other phenotype (median = 6, maximum = 328). We show how high-dimensional molecular phenomics data sets can be leveraged to accurately predict phenotypic variation between strains, often with greater precision than afforded by DNA sequence information alone. These results provide new insights into the spectrum and structure of phenotypic diversity and the characteristics influencing the ability to accurately predict phenotypes.