I’m currently using Mendeley[1]. Previously, I used Papers[2]. Unfortunately, the latest version of Papers (3.x) is terrible compared to how slick the old version (2.x) was. I’ve tried ReadCube[3], but somehow I find Mendeley easier to work with. I used EndNote[4] before I discovered Papers, and wouldn’t recommend it. I keep all my .pdf files in Dropbox.
Discussions/recommendations for papers:
In-person, well run, reading groups still seem to work best. Although I’ve seen good discussions on /r/maths and /r/physics on Reddit. ResearchGate[5] is useful for finding recent papers, while Mendeley is good for more historical connections.
Reading papers:
I’ve tried a Kindle, but having to convert with Calibre adds too much friction to the process, and the result still isn’t that easy to work with. Reading for long periods of time on a laptop or desktop monitor is painful. An iPad with a Retina display comes close, but old school paper printout still wins the day. You can carry paper anywhere and scribble annotations on it with ease. I also find being able to have multiple pages “in view” at the same time is sometimes helpful for understanding. Not easily (cheaply) done with iPads or laptops.