Many years ago I told a science librarian that electronic journals would never replace paper journals. Reading papers on a computer screen was simply too uncomfortable, and printing paper copies simply transferred costs from the library budget to the departmental budget. I was completely wrong. Not only has the advent of laptop computers made reading on computer screens comfortable (now I can read them in bed), but the ubiquity of electronic journals, internet mathematics archives, web course notes, and even Wikipedia has dramatically accelerated the pace of mathematical research and lowered barriers to entering new fields.
Before the internet, whenever I encountered an unfamiliar mathematical concept, I traipsed to the library, pulled books on related topics, and searched though their indices for a discussion of the concept in question. If the concept was too young to be covered in a monograph, I would chase through a maze of references in journals, one paper leading me to another until I mastered the desired concept. Now Google replaces this many hour endeavor with a rapid download of pdf files of relevant materials. Reading the papers might still be time consuming for complicated theoretical constructions, but finding the materials requires vanishingly little time. For a forgotten elementary definition, Wikipedia does the trick.
The advent of the mathematics arxiv led to an explosion of papers, often with results many might deem too insignificant to merit a paper. The downside is clutter on the web. The upside for my work is that with a quick flick of Google, I can find useful mathematical building blocks, which even though not deep, may save me from spending a week or more working out the details myself. Effectively, this makes research more collaborative.
The publication of minor results coupled to a rapidly searchable arxiv has dramatically quickened the pace of research. A researcher can now spend the bulk of his time at the leading edge of discovery (where admittedly the pace of progress often slows again), instead of trudging back and forth from the library.