The size of the testes of human males suggest that human females are relatively monogamous. They are closer to those of Gorillas than those of the Chimps. This suggests to me reduced sperm competition in humans.

Human females on the other hand don't have a clear physical indicator to give insight into male monogamy. anecdotal accounts say less so. Although some studies suggest male cheat is on par with female infidelity.

Historically there have been more polygamous cultures than monogamous ones. (for what that is worth.)