We hold a weekly journal club. It is called "the Brain Club." I regard the reading of journal papers as an important part of the education for graduate students. At first, it might take even a week to understand the significance of a paper, and present it to the lab members. As you get accustomed to the genre, you start reading the paper very rapidly. When you are thoroughly accustomed, you may be able to read a typical neuroscience paper in 10 minutes, and tell the gist of it to your colleague.
I got my Ph.D at University of Tokyo under the supervision of Dr. Takeyuki (Taki) Wakabayashi. Taki did research a few years at the Medical Research Council laboratory in Cambridge, United Kingdom. Taki used to say that Francis Crick read a lot of papers. On Fridays, Crick would take loads of papers with him to read over the weekend.
Training yourself to read lots of research papers is fun, and I whole-heartedly recommend it to people of high intellectual aspirations. Nowadays, it is very easy to do, as many papers are available on the internet for free. You don't have to belong to a university, or any institution whatever.