Understanding the nature and extent of horizontal pleiotropy, where one genetic variant has independent effects on multiple observable traits, is vitally important for our understanding of the genetic architecture of human phenotypes, as well as the design of genome-wide association studies (GWASs) and Mendelian randomization (MR) studies. Many recent studies have pointed to the existence of horizontal pleiotropy among human phenotypes, but the exact extent remains unknown, largely due to difficulty in disentangling the inherently correlated nature of observable traits. Here, we present a statistical framework to isolate and quantify horizontal pleiotropy in human genetic variation using a two-component pleiotropy score computed from summary statistic data derived from published GWASs. This score uses a statistical whitening procedure to remove correlations between observable traits and normalize effect sizes across all traits, and is able to detect horizontal pleiotropy under a range of different models in our simulations. When applied to real human phenotype data using association statistics for 1,564 traits measured in 337,119 individuals from the UK Biobank, our score detects a significant excess of horizontal pleiotropy. This signal of horizontal pleiotropy is pervasive throughout the human genome and across a wide range of phenotypes and biological functions, but is especially prominent in regions of high linkage disequilibrium and among phenotypes known to be highly polygenic and heterogeneous. Using our pleiotropy score, we identify thousands of loci with extreme levels of horizontal pleiotropy, a majority of which have never been previously reported in any published GWAS. This highlights an under-recognized class of genetic variation that has weak effects on many distinct phenotypes but no specific marked effect on any one phenotype. We show that a large fraction of these loci replicate using independent datasets of GWAS summary statistics. Our results highlight the central role horizontal pleiotropy plays in the genetic architecture of human phenotypes, and the importance of modeling horizontal pleiotropy in genomic medicine.