I used to be in the "let them name a number first" camp, but now I think differently. Unless you're looking for a first job you are probably already employed. So...what number will make you jump? That's your number.
There was a very similar question on Metafilter just yesterday[1], and this answer summed it up:
"Whenever I hear a candidate dither about specifying pay, I know they are either extremely flexible about pay, don't know the market very well, or don't value themselves very well. I know they will be willing to accept a lower amount than I would otherwise be able to offer.
In other words, if you don't specify a number, I'll specify one for you - and it'll be at the low end of what I can offer, not the high end. The highest paid candidates are the ones that know their value and refuse to work for less than their value. Most of those highest paid candidates are the ones that don't even bother giving a range of pay and simply say, 'I will work for $x'."
And, if it turns out your number doesn't result in an interview, then you've both saved a lot of time and a potentially huge dent to your salary curve.
So, as the above says, know your market and know your worth.
What number will make you jump ship doesn't necessarily match your market salary. If you're in a big-co and want to switch to a startup, you'll take a salary hit. If you just want out of your job because it's dead-end or your boss is a psychopath, any number may do.
Let's assume you want a market salary -- you can still know your market and know your worth but let them name a number first.
The assumption is generally if an employer names a number first it's going to be on the low end of their scale. Therefore, there is room up to negotiate to get to your actual value.
Suppose hypothetically you know your worth to be $120K. You don't say anything, and the employer comes out with $100K. You can negotiate for that other $20K since you know what your worth is. If money isn't a factor ("extremely flexible about pay") or if they really can't pay you that much, you can negotiate on secondary benefits like vacation time, reimbursements, and travel/training budgets. Would you take $110K and $15K of benefits instead of a $120K salary and $2K of benefits? Some people might.
Suppose you did say $120K, they can still try to price you down by price anchoring you to their initial offer of $100K. They'll go into the benefits, the intangibles, and the value of their benefits relative to the compensation -- how the "catered daily lunch" is actually like $X of salary for example. Maybe you go back and forth on negotiations and end somewhere around the first scenario.
Another way this could go is you state your salary, and their lowest offer was above yours. While it could be attributed to not knowing the market or valuing yourselves, it could be because you don't know their salary bands. This company either really wants you or just plain pays more than "market". If they're thinking $130K and you say $120K, you'll lose out on $10K/year.
I agree with this approach more than the common wisdom on this site that you should not name a number first. Pick a salary that you would be happy making given the desirability of the job, your current employment situation and the market. Quote that number and see if they accept. If they do--great! You have the job at the salary you want. If not, then consider their counter-offer and decide if that's something you want to accept.
The hiring managers for most jobs are not business owners. They are middle managers with multiple bosses. Most see the hiring process as an opportunity to show they are management material. If you give them a number that they know you will accept, they can pull whatever levels need to be pulled in the organization to get approval. What they don't want to happen is that they overbid for a candidate who then still rejects the offer. That makes them look incompetent in front of HR and upper management. Most managers would rather just give you a safe offer that you are more likely to reject than a politically risky one that might still get rejected.
There was a very similar question on Metafilter just yesterday[1], and this answer summed it up:
"Whenever I hear a candidate dither about specifying pay, I know they are either extremely flexible about pay, don't know the market very well, or don't value themselves very well. I know they will be willing to accept a lower amount than I would otherwise be able to offer.
In other words, if you don't specify a number, I'll specify one for you - and it'll be at the low end of what I can offer, not the high end. The highest paid candidates are the ones that know their value and refuse to work for less than their value. Most of those highest paid candidates are the ones that don't even bother giving a range of pay and simply say, 'I will work for $x'."
And, if it turns out your number doesn't result in an interview, then you've both saved a lot of time and a potentially huge dent to your salary curve.
So, as the above says, know your market and know your worth.
[1] http://ask.metafilter.com/274907/Minimum-salary-Really