Do people really counter with salaries that are 50% higher than the initial offer? Maybe it is just the nature of the employers I have dealt with in the past, but I have always felt anything in excess of the 5% - 10% range just meant that you and the company were too far off in expectations for a deal to work. In fact, a few months ago I rejected a seriously lowball offer where the difference was similar to the numbers you posted; I didn't even bother to counter. Is it really common to get companies to move by double-digit percentages on initial offers?
Edit: I should point out that people at this company had already told me how hard it was to find qualified people. There were plenty of other indications that they could not afford to be throwing away candidates.
When I joined Yahoo a decade ago, for example, I ended up accepting an offer 40% over the top of the advertised range, after demanding more. When they gave me the 40% offer, they apologised that they really couldn't go higher (it'd push me too far up over some other people in the department) and offered me more options instead, and guaranteed me a review after 6 months instead of 12 to bump me up further (which they did).
I've never taken a job at only 5%-10% above initial offer, and don't think I ever will - I know from my own hiring that we're always prepared to stretch more than that if we've first decided on a candidate.
After several rounds of interviews, they actually came back with an offer for much higher (they did ask me how much I am expecting to get paid before making the offer). I countered back and definitely got a salary offer that was certainly way more than 50% of the original intended offer and about 30% more than the actual offer they actually ended up making in their initial pitch.
Plus, unless you want the job very badly, it (usually) doesn't hurt to ask.
The particular case I mentioned was complicated because: a) the initial offer was knowingly less than I currently made; b) I previously worked for the parent company of the company making the offer and the offer was the same salary grade and almost the same salary I had when I left 2.5 years before. I'm not sure I would have tried to negotiate even if I thought I could get them up 30% - 40%.
Someone once said to me that sales is about desire and the price. If a customer desires something then the only reason they won't buy is price. In this case you're the goods and the salesman.
Assume that since you've gotten to the negotiation phase, you've exceeded their expectations.
Ask, 'how many people are you hiring?' If it's more than one, at the same position, then they may have more demand. It also may imply that their budget for hiring is above average.
Ask, 'how difficult has your interviewing been?' If it's been difficult, and you've reached this stage, then your in a better position for negotiation.
Ask, 'what have been your main criteria in hiring?' If it points to a rare skill that you have or some background experience or knowledge that is unique, then you're in a better position.
Ask, 'are there any other candidates that you're interviewing, and how do I measure up?' If there are no other candidates, and/or you're the best candidate that they have, then you're in a better position.
Ask, 'do you have upcoming milestones or deadlines?' If so, then may have higher immediate demand.
Ask, 'what are your goals in hiring me?' If they want to put you to work immediately, then you're in a better position. If they are primarily interested in grooming you, they may have more patience to hire.
Ask, 'who approves the hiring, and are you able to hire me today?' If someone else approves, it may be a harder negotiation. If they can hire you immediately, then you're in a better position.
Finally, don't set your price, first. If they ask, 'what is your price?', ask them 'what is your typical range for this type of position?' Get them to offer their price first because it's always on the lower end of what their range is. Then, consider your position. Ask for something that is slightly outrageous. For example, let's say you determine that you're in a good position. They offer you 80,000. Say that you were thinking more in the 120,000 range. Read their reaction to that. If they seem offended, say 'but, that can be negotiable, based on your benefits, etc.' Then, talk to them about the other benefits of the position, and come down slightly. But, once your initial price is set, that will be the baseline for further discussions.
Always come to the table with as much information as possible.
Always ask for add-ons. Ask for more non-financial benefits. Ask for more vacation. Ask for a more flexible schedule. If it's a big company, you're not in a good position to ask for extras, however.
Tell them that you'll give them an answer very soon, and set a specific date. It will show that you're serious. If you plan wisely, you can have multiple offers from different companies at similar time. Use these other offers to both gauge the demand and to play each offer against other offers.
And, remember, it's always supply and demand.