== tests for reference equality (whether they are the same object).

.equals() tests for value equality (whether they are logically “equal”).

Objects.equals() checks for null before calling .equals() so you don’t have to (available as of JDK7, also available in Guava).

String.contentEquals() compares the content of the String with the content of any CharSequence (available since Java 1.5).

Consequently, if you want to test whether two strings have the same value you will probably want to use Objects.equals().

// These two have the same value
new String("test").equals("test") // --> true 

// ... but they are not the same object
new String("test") == "test" // --> false 

// ... neither are these
new String("test") == new String("test") // --> false 

// ... but these are because literals are interned by 
// the compiler and thus refer to the same object
"test" == "test" // --> true 

// ... string literals are concatenated by the compiler
// and the results are interned.
"test" == "te" + "st" // --> true

// ... but you should really just call Objects.equals()
Objects.equals("test", new String("test")) // --> true
Objects.equals(null, "test") // --> false
Objects.equals(null, null) // --> true

You almost always want to use Objects.equals(). In the rare situation where you know you’re dealing with interned strings, you can use ==.

From JLS 3.10.5. String Literals:

Moreover, a string literal always refers to the same instance of class String. This is because string literals – or, more generally, strings that are the values of constant expressions (§15.28) – are “interned” so as to share unique instances, using the method String.intern.