I like using some kinds "worksheets" in the classroom. I usually use them to prepare students for vocabulary tests. I try to get them to illustrate a word with a small picture, and sometimes I even give a review (not worth a lot of points) so that they can use pictures I provide (graphics) to define the words. It's more work for me, but some students are visual learners and some are auditory learners. I worry about the visual kids when we discuss things, but feel that everybody gets some benefit from some kind of review that is entertaining and valuable. If they remember the picture, it may well help them to recall the definition.
I also have students make up their own worksheets, in a way, by having them draw pictures recalling the highlights of stories we read from The Odyssey. We read the stories from the text, discuss them, offer suggestions on how we could represent some of the creatures (e.g., Charybdis), and I never grade on whether they can draw. If they use colors, I give a couple extra points; students also need to summarize each picture with a sentence or two. I don't mind stick figures or speech bubbles that explain what's what in a picture.
Busy work? I don't do it. Kids resent it and I can't find any educational value for it. Answering valid questions, using crossword reviews, etc., I find sticks with kids more than filling out a paper. If my kids are not engaged by my work, they won't be engaged in my class.