Bill Wagner, fellow RD, and author of the excellent 'Essential C#' has an article on Code Project that debunks the conventional wisdom that String.Equal is better than Operator == for strings:

... for the string class, Operator == and String.Equal() will always give the same result. Period. You can use either interchangeably without affecting the behavior of your program. Which you pick will depend on your own personal style, and the compile-time types you're working with.

The == operator is strongly typed, and will only compile if both parameters are strings. That implies that there are no casts or conversions inside its implementation.  String.Equal, on the other hand, has multiple overloads.  There is a strongly-typed version, and another version that overrides the System.Object.Equals() method. If you write code that calls the override of the Object version, you will pay a small performance penalty. That penalty comes because there is a (slight) performance hit for the virtual function call, and another (slight) performance hit for the conversion. Of course, if either operand has the compile-time type of object, you'll pay for the conversion costs anyway, so it doesn't much matter.

The bottom line on equality and strings is that if you use the method that matches the compile time types you're working with, you will certainly get the expected behavior, and you'll likely get the best performance. If you want all the details, see Item 9 in Effective C#.

I'm posting this because I've had this discussion a few times and believe that Bill's explanation is the best I've seen.