Answer by Igor Markov:
Being old-fashioned, I keep things simple.
For a given project, you are unlikely to use more than 30-40 references. So, save the PDFs in a directory, with some clear file names (that include publication year, some indication of who the authors are, maybe the journal acronym, maybe also a keyword or two). If this gets unwieldy, partition papers among subdirectories/folders. If you are working with coauthors, share those (sub)directories on Dropbox or Google Docs. This should be enough, if your memory is reliable (if not, then managing PDFs is probably the least of your problems 🙂
When working on a dissertation, you need more than 30-40 references, but you also have more time. It is common to synthesize a dissertation from several pieces of work that are on the scale of publishable papers. Divide and conquer!
There are several nicely-designed online systems for managing references, but I find them unnecessary, limiting and distracting. Students spend time uploading papers, annotating them, etc, instead of actually doing research and working on their own draft. There are also things that these systems do not do, so the result is often a bloated and disorganized reference list with inconsistent formatting.
Managing references and citations takes such a small fraction of overall effort that you can just type the references in (you do need to understand how to format them, but that is explained in style manuals; or you can just carefully read papers from top science journals that edit papers rather than just reprint them).
Personally, I don't even use BibTex with my LaTeX papers.
When someone does, I can usually tell by noticing errors introduced by BibTex.