When I was growing up in the 60's and 70's it was the Russian magazine Shakhmatny Bulletin according to Bobby Fischer. In our chess club we generally believed that the reason the club's best player was the best player was because he had a subscription. He was a lecturer (or what Americans call a professor) in Russian at Durham University and translated into English most of the chess books in your library by Russian authors (Kasparov's My Great Predecessors, for example).
For Kasparov it was Chess Informant from the former Yugoslavia.
What characterized these two publications was that they were mainly just game scores of the strongest players around the world, mostly east European. Although Shakhmatny Bulletin was in Russian since the games were unannotated you really only needed to know the Russian annotation for the pieces. Informant was completely language free.
Nowadays there is little call for such games collections because we all have chess databases with online updates from The Week In Chess and ChessBase. What we want in a chess magazine is top class analysis of the best games and the latest inside news. The nearest I can come up with today is the Dutch magazine published in English, New in Chess, but all I have to compare it with are more parochial English magazines like BCM and Chess. I've never even seen a copy of the American magazine Chess Life, for instance.
When I lived in Germany I used to occasionally read a German magazine called Kaissiber which I thought was very good but rather difficult since it was in German.
Is NiC currently the best chess magazine out there? Or should I be reading something else?