If your current salary is competitive with the job market you're discussing for, then sure share it. Recruiters will try to give you a little more, but not less.
If your current salary is not competitive, and you're looking for a big gain, then you might be more inclined to just get the job and take the big jump, even if it could be bigger if you didn't provide that number.
If you're just starting out and focusing more on getting a job, and not "shooting yourself in the foot" in regards to compensation I'd look inward to see what sort of pay you'd take or need, and compare that relatively to the current job market to get an idea of what you should want/need and what you should expect. At this point you can tell the recruiter what you'd see fit.
I personally usually give out my current pay, but do give out a number of what I'd expect by doing my own research.
Everything is relative.
If your current salary is competitive with the job market you're discussing for, then sure share it. Recruiters will try to give you a little more, but not less.
If your current salary is not competitive, and you're looking for a big gain, then you might be more inclined to just get the job and take the big jump, even if it could be bigger if you didn't provide that number.
If you're just starting out and focusing more on getting a job, and not "shooting yourself in the foot" in regards to compensation I'd look inward to see what sort of pay you'd take or need, and compare that relatively to the current job market to get an idea of what you should want/need and what you should expect. At this point you can tell the recruiter what you'd see fit.
I personally usually give out my current pay, but do give out a number of what I'd expect by doing my own research.
Finally, a sensible, mature answer!