Should I sign a non-competition clause in freelance contract?

I have signed a few of those. As others have said, I make sure that they are very narrow in scope .. i.e. I can not develop a 'clone' of the application for another company .. short of that, I don't sign them.

The other thing to consider is that a non compete is essentially a value-add on your part. You give them more value for their money by signing one. So, they should be compensating you a bit for whatever projects you CAN NOT do in the next 3 years due to signing the agreement in addition to the actual project cost.

Usually, when I remind a company of this, they forget about the non compete and are content with trusting my ethics + an NDA.

It's not uncommon, but make sure it has some sort of expiration specified. Once you get established in a particular field or market, it's quite likely you'll want to continue in that market.

They're common. If you can get them to remove it, do so. It's never in your interest to have one. That said, they aren't terrible if they are narrowly scoped and of a reasonable time limit. You don't want one saying you cannot write any other iPhone apps. One saying you can't write the same sort of app is probably acceptable. Read the language and determine how broadly it can be viewed.

Whether you end up having to sign one or not depends largely on the power in the relationship. If you really need the work or if your skills can't command a lot of respect, you'll have to sign. If, on the other hand, you bring unique skills and the company really wants you, you have leverage and can likely get it removed.