First of all, let me say that for the question above, I would answer like a politician - maybe and sometimes. I believe that homework is essential to learning - Marzano backs this up with research, but I think it needs to be purposeful in order to be effective. I also believe it should be a minor component of the actual grade. In my class, 75% of the students' grade is based on their assessments. 25% comes from other sources - mainly class activites and homework.
As a senior in high school, I received the highest grade in my physics class. I never took math past geometry and had no idea what I was doing in physics. I was able to keep a meticulous scientific journal and give great powerpoint presentations. Powerpoint was new then and I sort of "dicovered" it while messing around in the media center and impressed my teacher with my use of it.
My future husband was in that class. I received the highest grade, but he was the physics master. He would often re-teach the class if we didn't understand our teachers presentation and went on to major in physics at college and be published in a mathematics journal for his supreme mathematics and scientifc understanding. His journal, however wasn't as nice a mine and his presentations simpler. He did have a better mastery of the material in the class. He should have had the top grade.
Recognizing this, our teacher did award us dual awards that year (which led to catcalls at the awards ceremony since we were dating). I don't believe he would have had to do this if his class had been graded based on actual mastery and understanding of the material. He awarded way too many points for assignments that did not actually reflect understanding of the material.
So, how do you grade homework? How do you grade other assignments?
As a side note, I do assign homework. I tell students that it will not impact their grade in and of itself in a significant way, but that by completing the assignment they are receiving valuable practice for the assessment which will make up the majority of the grade for the class. Doing this saves me grading time (since I am not grading homework every night )but then I also believe it helps the grades in my class reflect actual understanding of the material.