How do you respond to a request for 'emergency contact information' for when you are on vacation?

Question

I want to go on vacation and not think about work at all but they want me to provide them a contact number in the event of an emergency (server goes down, web service malfunctions, etc). I am afraid that it will be abused (they will contact me before trying everything for example) but I also think that if I am on vacation I should not be bothered even if there is an outage. Does anyone have experience with situations like this? What's the tactful approach? Any creative solutions?