It varies hugely, depending on the industry (a game developer might have very different responsibilities from someone who works at an ISP like Comcast or Verizon, for example), and depending on the team of people they are working with.
For me, on any given day I'm usually in the middle of improving an existing piece of software. Most of my projects take multiple days to weeks to complete. Today, I am just finishing up making a small change that a customer who uses the program I work on asked for. I am also adding a new ability to a program that I wrote over the past year. Finally, I am working with another software engineer to make a plan for how we're going to clean up a very messy piece of code over the next week or so. This last one means writing a document describing "Here's what we hope to accomplish, here's how we think we're going to approach it, and here's what might go wrong." It isn't writing code, but it's still an important part of the process.