I just use Cmd+H to hide windows instead of minimizing, since hiding effectively does exactly what I want (get the window out of my sight, but leave the app running) and then I can easily Cmd+Tab back to it.

I only recently found a good use for minimizing over hiding: I was working in my IDE (PhpStorm) on several projects (each project opens in its own window) and I wanted to switch back and forth between two project windows. With 4 or 5 windows open, switching between the two windows I was interested in (using Cmd+`) was a game of cat and mouse. I was alway hoping that I'd land on the right window and not mess up the order of windows. Then I realized if I just minimize the windows I don't need right now, I can get them out of the Cmd+` cycle and easily switch between on the two windows I want.

I knew about it pretty much from the beginning, but I still never minimize anything since it's a pain to have to remember which windows I minimized and therefor need to also press Option for.

Of course more often then not I'll use Alfred, which does open minimized windows by default.