Many times I run complex commands to automate tasks, and due to the nature of these commands I log the output of them. As an example, the command that gave me this idea is as follows
export MODELDIR=$PWD ; for x in coref namefind parser; do cd "$MODELDIR/$x"; echo "$x" >> "$MODELDIR/download.log"; wget -c `<list` >> "$MODELDIR/download.log" 2>&1; done; cd "$MODELDIR"
Since it downloads a lot of files from lists, and can take quite long. Doing this I would want a log of any failures, and normal terminal output history won't cut it.
But even though it's a log I open a second terminal and tail-follow this file.
So, I'm using it as a log for reference when I move away from the computer, but ALSO as output to watch it's status.