Ever since starting graduate school I've tried to make scientific reading a part of my daily ritual; I track pages read using Beeminder, and the graph doesn't lie. It keeps me honest.
I aim to closely read and summarize 5 pages per day and skim a few other abstracts besides that. I spend about half my time looking at data and figures which doesn't contribute to my daily "page count." When I'm reading about a new topic these five pages can take several hours, but on topics I have more background in five pages might only take an hour per day.
I guess since everybody defines "read" in a different way it's hard to get an objective answer about how much reading is enough. How much people read seems like a bit of a sensitive topic among real-life colleagues because everyone has a bit of anxiety that they aren't reading enough. But for those further along in their academic path, I'd like to hear how you approached the literature early in your graduate school career and what you think is a sufficient amount.
I guess this all distills down into two main topics:
When deciding what to read each day, should I focus on depth or breadth?
Is five pages of close reading per day enough? I know it doesn't sound like much, but it takes significant mental energy to meet that goal. And consistently reading 5 pages per day adds up to a lot over time.
Edited to add: I mostly read about petrology, volcanology, structural geology, and tectonics if that makes a difference. By "page" I mean "page of text" so if I'm reading a structural geology paper with lots of maps and figures I discount for those and a "ten page" paper becomes a 5 page paper for my purposes.
Answer
My experience is almost exclusively with mathematics papers, and applies little or not at all to other fields.
Much of eykanal's post applies to math as well, but one big difference is that math papers are much more varied in their structure, not having an actual experiment to tie them together. A good paper will generally explain its organization in the introduction, however.
One point worth emphasizing is that reading a paper from front to back, trying to understand everything at each step, is usually inefficient. The most common instance is that a paper often starts with definitions which may be hard to make sense of without understanding the theorems they're used in. It's generally more effective to skim the paper several times, trying to understand more and more with each pass.
Relatedly, you'll eventually pick up the skill of picking out the most interesting ideas from a paper without reading the whole thing. Early on, though, it's probably better to read things carefully; it's very easy to fool yourself into thinking you've understood something.
As to your main question, about breadth versus depth, your first priority has to be depth, because that's what you'll ultimately need to be able to do your own research and get your degree. But if you're learning enough to do that, you want as much breadth as possible. It actually gets harder and harder to learn completely new things as you get on in your career, even when there may be direct benefits to your research to do doing so. Laying the foundations of a broad understanding of your field while in graduate school will pay off later.
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