Factoid for the day: cockroaches seem to have been morphologically stable since the Carboniferous, i.e. over the last 290 to 354 million years.
Modern cockroaches are more similar to their ancient fossil ancestors than any other extant insect - except they are a lot smaller. Some cockroaches from the Permian (about 250 million years ago) were over a foot long. Wouldn't want to step on that at night - it would go like a skateboard!
I haven't seen it in the movies, but most ships in history have had very serious cockroach problems because of the lack of predators. Captain Bligh had the Bounty doused with boiling water to deal with this. We have a cockroach problem at the South Pole's Scott Base in Antarctica for the same reason.
They were among the few creatures to make it through an ancient disaster event called the Permian-Triassic boundary, where 90% to 95% of marine species went extinct, as well as 70% of all land organisms. On an individual level, perhaps as many as 99.5% of separate organisms died as a result of the event. But cockroaches made it.
Other things that made it through and became more important as a result: mosses and worts, therapsids (where we come from), and bivalves.