US employee here - I've signed one (plus a patents & inventions at one firm) at every firm I've worked at since 2000 or so. Thus far any side projects haven't been a problem for them, as I have made sure to target a different industry. But legally, they could have enforced the contract and taken possession of my code.
Even winning a lawsuit costs a lot of money and stress. Unless there is a law that makes courts throw out frivolous lawsuits immediately the employer with lawyers on staff still can make your life very difficult