Over the 180 million years since their origin, the Y chromosomes of mammals have evolved a gene repertoire highly specialized for function in the male germline. The mouse Y chromosome is unique among mammal Y chromosomes studied to date in that it is large, gene-rich and almost entirely euchromatic. Yet little is known about its diversity in natural populations. Because the Y chromosome is passed only through the male germline and is obligately transmitted from fathers to sons without recombination, it provides a rich view into male-specific mutational, selective and demographic processes. We therefore took advantage of a recent high-quality assembly of the mouse Y to perform a systematic survey of a diverse sample of Y chromosomes using published whole-genome sequencing datasets. Sequence diversity in non-repetitive regions of Y chromosomes is <10% that on autosomes and the site frequency spectrum is skewed towards low-frequency alleles, consistent with a recent population bottleneck. But copy number of genes on the repetitive long arm of the Y is extremely variable: the total size of the Y chromosome varies by two-fold within Mus musculus and three-fold between M. musculus and M. spretus. We show that expression of Y-linked genes in the testis is rapidly evolving in murid rodents and especially within M. musculus, and is consistent with ongoing intragenomic conflict with the X chromosome. Our results provide insight on the demographic history of an important model organism and the biology of a rapidly-evolving sex chromosome.