C# difference between == and Equals()

Question

I have a condition in a silverlight application that compares 2 strings, for some reason when I use == it returns false while .Equals()

Answer 1

Really great answers and examples!

I would just like to add the fundamental difference between the two,

Operators such as == are not polymorphic, while Equals is

With that concept in mind, if you work out any example (by looking at left hand and right hand reference type, and checking/knowing if the type actually has == operator overloaded and Equals being overriden) you are certain to get the right answer.