When I was growing up we didn't have home computers let alone PlayStation to entertain ourselves. Handheld camcorders were barely coming to the retail market by the time I was in 8th grade, but still a long ways away from the YouTube and Facebook arena we now see today. Times were extremely different back then and so was school.
In other words, they never memorized their multiplication tables! Many times I have seen a student do poorly due to a weakness in basic math facts they should have learned in third grade.
However for the most part, when a worksheet is needed to help drill down a procedure, standard, or lesson, its effectiveness can and will vary.
Worksheets also, when used properly, provide both the students and parent / tutor immediate feedback as to the child's progress. This means they can be used to point out areas where the student needs further reinforcement.