Are faculty salaries negotiable in general? Wherever they are negotiable, how could applicants gain insights about the statistics of offers or the extent of safe negotiation?
This entire answer is US-centric, since I have no clue how other countries work. This is not to say that I know the US system that well - but rather that it's the only system I know at all.
Public universities work differently from private universities. Public universities usually have pay scales and these are often public since professors are considered state employees (yes, my salary is public knowledge). So you can start digging around there. Usually there's a range within which you can hope to negotiate: moving out of that range is beyond even the power of the university to authorize.
Private universities usually have more flexibility and it might be harder to get the range of salaries. But if you get an offer you can ask around to get a sense of the ballpark.
As for what a reasonable range is, getting data is very discipline-specific. For CS, the CRA puts out stats fairly regularly and there's the Taulbee survey. For other disciplines, there might be something similar.
Salaries in academia at least at tenure-track level are less flexible in general. Probably the best way to get to the top of the permissible range is to have another offer. Other than that it's hard. Often, the things that are most easily negotiated are other parts of the startup package. Which is not to say that you shouldn't negotiate salary - but unlike in industry, it's less likely to be as beneficial.
This answer applies to Belgium, or perhaps just Flanders.
Academics are public servants, so the pay scales are fixed. The only thing that is flexible is where on the scale you start. This is then based on the number of years of relevant experience, which is often counted as the number of years after your masters. They will probably apply some tricks to bump it down a notch or two, while appearing generous. No room for negotiation, though.
This answer applies to Australia.
Base pay rates are set by a Federal "Award" which fundamentally covers all academics working in Australia. An employer and employee can privately negotiate an above award wage or condition, but this is never done (employer resistance).
Most academics are covered by a site specific Enterprise Bargaining Agreement negotiated by the union (NTEU) and the employer. This sets graded minimums based on the career phase of the academic, and covers all kinds of academic labour from casual tutor through to professor (a terminal, demonstrated high research output position with field leadership responsibilities). The persons not covered under this are management. The employer is generally unwilling to negotiate variations except for professors and management. Each pay rank has an internal series of steps (Lecturer step 1, step 2, step 3, etc.) representing increases in income based on years of service.
While academics of all disciplines are paid the same at the same grade, the Enterprise Bargaining Agreements vary from site to site, so academics at one University in Melbourne will be paid less than another in Canberra but more than another in Sydney.
In the UK/England, the scale is fixed. There is a "London allowance" which, again is fixed, that I believe is not counted as salary for tax and pension purposes. Your salary increases ~2.5% for each point on the scale you move up.
Each university sets the starting point at which they appoint lecturers (assistant prof equivalent) as well as the maximum point you can progress to without promotion. There is some variation in this range across universities, but within a university it is fixed. I think most universities/departments appoint new lecturers at a 2 points above the bottom of the scale. Sometimes you can negotiate to move up another point or two.
Here is an answer for Germany.
In Germany there are three different types of professor salaries: W1, W2 and W3 (unfortunately there is no English Wikipedia site...).
For W2 and W3 the salary is negotiable. In fact, the base salaries have been lowered when the W-system has been introduced (some 10 year ago or so) but there is now the opportunity to have variable bonuses. These bonuses can be obtained by various means and the precise procedure varies from state to state and even from university to university. Basically, one needs to show that one is a high performer, for example in research (having big grants, a lot of publications,...) or in teaching. Moreover, there is a raise for extensive service (e.g. for being the dean). You can expect a raise for sure if you get an external offer for a position which is at least equally good. I think that there are statistics about the average bonus a W2 or W3 professor gets but I can't find one right now. I am not aware of an upper bound for the total bonus and I think the bonus can get higher than 50% of the base salary.
For W1 professors (junior professors) the situation is different. Basically there are no bonuses but there can be exceptions. One needs to show different things and especially that the position could not be filled otherwise. Moreover, the maximum bonus is at 10%.
The Academic Careers Observatory may be a helpful resource, especially for the European countries.
For example, their information on the Finnish salary system is fairly accurate: there is a non-negotiable fixed base salary level that depends on your job title, but on top of that there is up to 46% extra that is determined based on your personal performance (i.e., there is a lot of room for negotiation, at least if you can show that you are actually doing your job exceptionally well).
First: Yes, salaries are negotiable.
The specifics of how much you can negotiate for will depend on a lot of things including flexibility on the institutions end and the amount of leverage you have in the negotiation (e.g., Do you have other offers? what else are you asking for? etc).
Ask around for details on other offers. I've seen folks on the Academic Jobs Wiki sharing details about offers and startup packages to give folks an idea of what is possible to negotiate for. Professional organizations will often publish these statistics as well.
One useful data point: Many public schools, at least in the US, are subject to public record laws. I know of people who downloaded the full database of salaries from public universities they had offers from, created the subset all the people with the title of the job they were offered, and used those data as a way of getting a sense of the range they could negotiate for.
One piece of advice I got early on was useful: If you are never told "no," you didn't ask for enough. So don't be afraid to ask. Of course, always be deeply respectful in the process and keep in mind their own limits and abilities. Your negotiating partners are your future colleagues and a good working environment is worth more than whatever you hope to gain in a rough back and forth over a few thousand bucks.
This answer applies to Canada.
There is generally a fixed pay scale in Canada. But you can always try to negotiate and sometimes it works. Especially, if someone moves from a faculty position to another university and the salary would be lower, then that person should negotiate to keep at least the same salary (the salary should not decrease). Besides, some top level professors may negotiate to get application for a research chair or that the university also hire their husband/spouse at the same university. This has been done in some cases. You can also negotiate to try to get a permanent position, etc.