I was very surprised to find out that printer could help a lot for some programming tasks. But first it was very unusual and I had to think a lot on how it could help.
So how do you use printer to improve your productivity?
P.S. I post my answers below.
It helps me a lot to study complex DB schemas. I just print a few (>=4) pages that give me more visual space than my working monitors and study them.
It helps to study a UI logic of a relatively big site. I just print all important pages and put them into a really big picture.
I also find it helps to print out presentations and other important documents like proposals or tutorials and lay them out on a big table or on the floor. Removing the restrictions of a 13" screen can be useful for spotting things that may not jump out at you otherwise.
Sometimes there just isn't enough screen real estate, no matter how many monitors you have. Printing out reference documents and code snippets can help.
I once taped a dozen sheets of paper on my wall so that I could look at all of a computer-readable logical proof (all-plain text, lisp-like syntax, small font size). Scrolling is not nearly as fast as turning your head once you know where all your code is. Find just doesn't always cut it.
Sometimes it might help to get away from the computer, and by printing some code or documentation it can be studied "offline".
For the ACM ICPC programming contest (3 people on a team 1 computer) it is very useful to print out code and debug it on paper while someone else types in code. I like debugging code on paper a lot because you can easily look at the the whole thing rather than what you are restricted to on a screen. I don't print out code that often outside of contests, but occasionally it is useful.
Print stuff out, get a red pen, lie down, spread the sheets out, and read through it all marking it up as you go with every infelicity you notice. Draw arrows from this to that; would it flow better rearranged? Etc. -- jot down any ideas that occur. Screens and keyboards still can't compete with paper and pen for what those are good at. Neither can sitting quite compete with lying down (though I've heard Eric Drexler suspended a monitor from the ceiling so he could work while reclining). I know, that bit shouldn't matter.
Print single-sided since having to flip sheets back and forth defeats the point.
This doesn't so much improve your productivity immediately (though it can help via the change of setting, pace, and affordances) as improve code quality, helping productivity over time.
When I have to review technical documents, like Product Specifications, Feasibility Studies and the like, I often find that I need to step away from the PC and get into a focused environment.
Printing out these documents and doing it the old fashioned way is an underappreciated skill, in certain situations.