Threatening to leave is also a reliable technique to stop ridiculous price hikes and even get hefty discounts.
Sometimes you have to talk to someone on the "retention team." At other times you can do it online. Most recently I preserved the NYT intro rate of $4 every 4 weeks (instead of $25) and I got a 33% discount on an Adobe subscription after they announced a 50% price hike and I started the cancellation process.