Most companies will have so much work that you will never run out of things to do. But there are times when you don't have enough to do. In this situation, you should ask your manager to give you more work.
Although asking for more work is a good sign of being productive, there is actually something better. Instead of asking for more work, find the extra work without asking. After you find something to do, then tell your manager that you want to do the work.
If you are a manager, would you want someone asking you what to do, or would you prefer a worker who found a problem and wants to fix it. I have had people ask me for more work and it is stressful trying to think of something. I am busy and don't have that much time to find extra work. If a worker identifies more work to do, then I would appreciate it that much more.