What do you do if students do not complete their homework on time, or if a student never completes his/her homework assignments? When should you contact the parents and make them aware of the situation?
I think contacting the parents immediately would be a good idea. This could potentially be linked to a problem of some sort at home. Hearing about any problems from the parents would allow you to be more understanding of the situation. If the student is just being lazy, or forgot then perhaps try giving a pep talk of sorts, explaining to them why homework is important or asking if they need assistance on it if it's too difficult for them to do alone.
It's hard to give a real definitive answer without knowing the age of the students. However, I would say that contacting parents sooner than later is probably the best thing to do. I think most parents want to know if their child is not completing work, even if they don't do anything about it. My general rule of thumb when relaying news to parents is to make sure there are no surprises when report cards and parent-teacher conferences come around. I think you also need to consider the student and try to determine the causes for not completing homework. Kids with ADHD, for example, often have huge struggles with homework completion.
I would certainly contact the parents. More times than not the parents are supportive. If you can't get the parents on board, maybe you can have the student work on the assignments during free time such as lunch. After a few times of working through lunch, maybe they will start doing it at home. I think it is good to talk to the parents, you never know what is going on at home. Maybe they are responsible for a younger sibling at night while mom or dad is at work.