Is it a bad idea to tell my coworkers that I'm looking for a job?

What's the general opinion on telling the people you work with that you're planning to leave?

I remember my dad gave me some advice to keep the fact that I'm looking for a job completely secret until I officially submit my resignation. His point of view was that you can't guarantee who might use this information against you. Honestly, I've always seen his perspective as a bit pessimistic.