Nothing, if people keep them inside, and do the right thing and get them spayed/neutered. They can control pests, but also (noting from your tag) will kill songbirds, etc.
Here's somebody's opinion. Well stated as a position, but perhaps not entirely accurate:..
The domestic cat, Felis silvestris catus, is quite probably the most useless animal on the planet and we have an estimated 10.3 million of them in the UK.
They spend 85 per-cent of their lives doing nothing, sleeping or dozing...
Eating, drinking, killing, defecating and mating take up just four per cent of their time and 11 per cent just getting around...