1 Emily: I like ruins. I went to Greece to see the Acropolis once.
2 Prof. Jones: Did you know that all the the temples on the Acropolis were designed by female architects, with no input from males at all?
3 Emily: Really?
4 Prof. Jones: Yes, there were all the product of Parthenongenesis.

Parthenogenesis is the asexual reproduction of organisms by means of embryo development from unfertilised ova.

In some cases it can occur in species that normally reproduce sexually, triggered by environmental conditions that may include a lack of male individuals for some reason. Species that have been observed to do this include aphids, mayflies, three shark species, some snakes and lizards (including Komodo dragons!), and several species of domesticated birds, including chickens, turkeys, and pigeons. The production of a fertile egg by an unfertilised female can be triggered by an error in DNA replication during the production of the egg, or as a normal occurrence, depending on the species.

Perhaps more surprising is that many species reproduce exclusively by parthenogenesis. Over 80 species of lizards are known to have populations consisting exclusively of females, who all produce viable young without any fertilisation by males at all.

The Wikipedia article linked to above contains much more detail, much of it in technical biology terms that I'm not qualified to summarise sensibly here. It's fascinating though.

Also: In actual fact the Acropolis temples were not really designed by female architects. The Parthenon was designed by the (male) architects Iktinos and Callicrates. There are many other temples and buildings on the Acropolis site, whose architects are uncertain, but it's very likely the designers were males too, given the social structure at the time.

The punning coincidence between "Parthenon" and "parthenogenesis" is not really a coincidence. Both words stem from the Greek παρθενος (parthénos), meaning "virgin". The usage in "parthenogenesis" refers to birth from an unfertilised ovum. The parthenon on the other hand is named after Athena Parthenos, the aspect of the goddess Athena as the virgin. (Also, Athena was born from the forehead of Zeus, with no mother, in an act of parthenogenesis.)

Reader Carl F. provides some additional points on parthenogenesis:

1. The only known species to be geologically old while using obligate parthenogenesis appears to be among the rotifers. It's rare in other animal groups, presumably because it isn't a good long-term strategy, since it makes genetic adaptation slower and adaptability lower by reducing genetic diversity to what one organism can carry. (Aphids and other groups use parthenogenesis when in rapid-population-increase mode, then switch to sexual reproduction when local resources become scarce.)

2. Some groups, most notably the hymenopteran insects (wasps, bees, ants) produce all males using parthenogenesis. Fertilized eggs produce females, unfertilized eggs produce males. A few other insect groups and even fewer arachnids use this system, along with sexually-reproducing rotifers.