In most cases not much will happen. they will probably sell our info to an off shore company that can use this info to scam people. For instance someone contacted my Email address and said they have a video of me "abusing" myself in front of my laptop. They had all my info. They wanted 1 BTC for them to not release my video online
It was one of the funniest thing. But probably they either hacked one of the ICOs I participated or something