Would you consider computers to have emergent systems? Simple parts interacting to give rise to complexity greater than the sum of those parts.
i.e. countless logic gates eventually culminating into the internet, videogames, or artificial intelligence.

I'm writing something on emergence and want to give some in depth examples but don't want to sound stupid using this as an example if its not one.

Some other examples I'm more confident about are economic markets, ant colonies and bird/fish flocking - but I'm trying to convey the idea that emergence is everywhere, not just in animals. I'm planning to mention consciousness as a possible example of emergence as well, if you subscribe to physicalism.