Coffee makers. I once picked up a nice, high-end Keuring machine for free from a neighbor. Later than evening, I noticed something moving around it. It was full of roaches. I put it in a trash bag and ran to put it in the garbage outside. The exterminator and landlord both said the warmth and moisture of coffee machines is a magnet for roaches and coffee is their favorite snack.

I once had found a nest of ants inside a laptop.

The laptop was on a table in the middle of a 40'x40' room but one day I came in, turned it on and for the next 15 minutes ant pieces flew out of the fan exhaust.

All it takes is one pregnant cockroach in a box somewhere. They will often hide in electronic devices.

Sprint sent me a magic box some years ago (It's like a cellphone repeater). UPS helpfully threw the box out in the snow where it was discovered a few days later. We installed it and bits of bug I'd never seen before started coming out. Turns out it was full of dead German cockroaches that presumably froze to death.

I live in a pretty rural area so the only ones I see sometimes in the summer that have hitched rides before are the virginia woods cockroaches that fly. But I've never seen them infest a house, they just seem to be attracted to the lights.

Corrugated cardboard (boxes) can be a vector for cockroach eggs. I once crewed on a yacht whose captain forbid any cardboard boxes to be brought aboard for this reason.

Step on one, eggs stick to the shoe and voila.