Because of its highly repetitive nature, the human male-specific Y chromosome remains understudied. It is important to investigate variation on the Y chromosome to understand its evolution and contribution to phenotypic variation, including infertility. Approximately 20% of the human Y chromosome consists of ampliconic regions which include nine multi-copy gene families. These gene families are expressed exclusively in testes and usually implicated in spermatogenesis. Here, to gain a better understanding of the role of the Y chromosome in human evolution and in determining sexually dimorphic traits, we studied ampliconic gene copy number variation in 100 males representing ten major Y haplogroups world-wide. Copy number was estimated with droplet digital PCR. In contrast to low nucleotide diversity observed on the Y in previous studies, here we show that ampliconic gene copy number diversity is very high. A total of 98 copy-number-based haplotypes were observed among 100 individuals, and haplotypes were sometimes shared by males from very different haplogroups, suggesting homoplasies. The resulting haplotypes did not cluster according to major Y haplogroups. Overall, only two gene families (RBMY and TSPY) showed significant differences in copy number among major Y haplogroups, and the haplogroup of a male could not be predicted based on his ampliconic gene copy numbers. Finally, we did not find significant correlations either between copy number variation and individual’s height, or between the former and facial masculinity/femininity. Our results suggest rapid evolution of ampliconic gene copy numbers on the human Y, and we discuss its causes.