Func - When you want a delegate for a function that may or may not take parameters and returns a value. The most common example would be Select from LINQ:
var result = someCollection.Select( x => new { x.Name, x.Address });
Action - When you want a delegate for a function that may or may not take parameters and does not return a value. I use these often for anonymous event handlers:
button1.Click += (sender, e) => { /* Do Some Work */ }
Predicate - When you want a specialized version of a Func that evaluates a value against a set of criteria and returns a boolean result (true for a match, false otherwise). Again, these are used in LINQ quite frequently for things like Where:
var filteredResults =
someCollection.Where(x => x.someCriteriaHolder == someCriteria);
I just double checked and it turns out that LINQ doesn't use Predicates. Not sure why they made that decision...but theoretically it is still a situation where a Predicate would fit.