This also depends on the nature of the organization you're negotiating with. The people first asking about your current salary / expectations of salary in a larger organization will often be from HR, collecting information that they'll feed up the organization, probably your boss-to-be's boss. The higher up this goes, the harder the heads are at negotiation; frequently, your boss-to-be, at the salary negotiation level, is just a go-between. He'll have an expected budget, but to push higher he'll have to go to his own boss, and that dynamic favours the company rather than the employee.

You need to balance the risk of getting off on the wrong foot, with the potential that you can be leaving a lot of money on the table - I mean, on the order of quarter of a million to half a million dollars over the course of your stay with that company is quite likely if you don't negotiate well - not to mention a bitterness that can grow over time. And switching jobs may not even be a cure here; if it's a job you enjoy, it's not much fun having to leave it in order to get your worth on the market. It's best to get both.