Nowadays researchers are generally not paid to review research articles. Has it always been the case? If not, how come it has changed?
You probably mean referees, those who referee papers for the journals. ("Reviewers" is the usual name for those who write the reviews for Math reviews or for Zentralblatt Math. They are payed small amounts per review.)
Some journals do pay to the referees. For example, Indiana University Math journal used to offer $50 per report, I don't know whether this continues. (Also notice that this always was one of the cheapest journals).
But of course this is an exception. Traditionally refereeing is considered a service to the community, and mathematicians do this voluntary. I suppose other scientists do this voluntary as well. As far as I know this always was the case. In general, fundamental science was not considered a commercial enterprise. Scientists are usually not payed for their published papers (though they may collect royalties for books). So it was assumed that can do the refereeing jobs on the same basis.