Sure. Just for a start, some of David Bailey's papers (http://www.davidhbailey.com/dhbpapers/), e.g. "High-Precision Arithmetic: Progress and Challenges" and "High-Precision Floating-Point Arithmetic in Scientific Computation" show some concrete examples. You will find many others by searching for papers containing the words "quad double arithmetic", "high precision arithmetic", "multiple precision arithmetic" or similar terms. Most applications are probably in physics, and of course in pure mathematics.