Today I had to track down a performance issue on a live site where the CPU usage was abnormally high. I couldn't reproduce it locally, and didn't want to install profiling tools on the live server (not that our IT team would have allowed this anyway!).
Whilst debuggers have become more and more powerful over the years, simple debug output traces certainly still have their place in many situations. Logging out information at certain points in your code can tell you a lot about what's going on, especially when trying to debug an issue.