Pleiotropy is the phenomenon where a single gene influences multiple traits, contrasting with polygenic traits where multiple genes influence a single trait. Key examples include Gregor Mendel's observations in pea plants, the vestigeal gene in fruit flies, and human disorders such as phenylketonuria and sickle cell anemia, which exhibit varied phenotypic effects from a single genetic mutation. Antagonistic pleiotropy describes scenarios where a gene can have both beneficial and harmful effects over an organism's lifespan.