When I was a referee (physics), it was most definitely not considered part of my job. I did it entirely voluntarily, was not paid for it, and no-one at my institution cared whether I chose to do it or not.
> and no-one at my institution cared whether I chose to do it or not
Are you speaking as a grad student, or faculty? Because if you don't review, sit on an organizing committee, or otherwise participate in the academic process in your field, you're not going to make it very far in your career. Our disciplines are smaller than you think, and people take notice, especially in your own department. Are you sure you don't have a reputation?
Thanks for your viewpoint. It is so different from the one that I saw (which field are you from btw?)
Both times I was asked to become a referee for a journal (during phd and then postdoc), it was because someone I knew was fed up of doing it, and wanted to pass it on to someone else. I volunteered because, like you, I knew someone ought to do it and felt that I should 'give something back' - especially because I liked the journals and had published in them. It was a (minor) distraction from my research (a couple of days every few months). The definite impression that I got from my colleagues (including more senior ones) was that it had little or no relevance to my career, compared to publications. It is not impossible that I misread the situation, but I doubt it. I would prefer the situation that you describe.
Interestingly, an economist I worked with (they tend to have a very slow review process) told me about an economics journal where you had to sign up to referee 1 paper for every paper you submitted, and pay a bond to ensure you did it. Just how one would expect rational economists to do it :)
Are you speaking as a grad student, or faculty? Because if you don't review, sit on an organizing committee, or otherwise participate in the academic process in your field, you're not going to make it very far in your career. Our disciplines are smaller than you think, and people take notice, especially in your own department. Are you sure you don't have a reputation?