A couple of years ago, a client of mine asked if I could stop writing about competitors of theirs. They didn't want me to mention them in lists (even if another client asked me to), and they were hoping that I wouldn't take jobs with clients that partnered with the competitor. In the end, I agreed to sign a non-compete for six months, and the client had to pay me extra to write articles for them since this made my life a little difficult.
In other cases, I've found non-compete clauses in contracts and have asked clients to take them out before I will sign. When you work in a niche like I do, almost everyone can be seen as a “competitor.” You don't want to sign a non-compete and then find that your ability to provide for your family is limited.
There are some instances when it might make sense. A friend of mine was asked to sign a non-compete when he sold is blog for seven figures a few years ago. He has to wait a set period of time before he can start another money blog. I know others who agree to limited non-competes when they have agreed to be brand ambassadors. There are times when it can make sense to sign a non-compete.
However, if you have a client that is just trying to limit you — as a freelancer — without being able to make up for your lost business compensation, you might be better offer refusing to sign and then working with a client who is a little more flexible and understanding.