Concise update for Java SE 9

Reference arrays are bad. For this case we are after a set. Since Java SE 9 we have Set.of.

private static final Set<String> VALUES = Set.of(
    "AB","BC","CD","AE"
);

"Given String s, is there a good way of testing whether VALUES contains s?"

VALUES.contains(s)

O(1).

The right type, immutable, O(1) and concise. Beautiful.*

Original answer details

Just to clear the code up to start with. We have (corrected):

public static final String[] VALUES = new String[] {"AB","BC","CD","AE"};

This is a mutable static which FindBugs will tell you is very naughty. Do not modify statics and do not allow other code to do so also. At an absolute minimum, the field should be private:

private static final String[] VALUES = new String[] {"AB","BC","CD","AE"};

(Note, you can actually drop the new String[]; bit.)

Reference arrays are still bad and we want a set:

private static final Set<String> VALUES = new HashSet<String>(Arrays.asList(
     new String[] {"AB","BC","CD","AE"}
));

(Paranoid people, such as myself, may feel more at ease if this was wrapped in Collections.unmodifiableSet - it could then even be made public.)

(*To be a little more on brand, the collections API is predictably still missing immutable collection types and the syntax is still far too verbose, for my tastes.)

String[] a= {"tube", "are", "fun"};
Arrays.asList(a).contains("any");

Convert your array to a List and than use the contains method.

List mylist = Arrays.asList(directions);
mylist.contains(input);

The contains method returns:

true if the list contains the specified element.

You could also use the commons-lang library from Apache which provides the much appreciated method contains.

import org.apache.commons.lang.ArrayUtils;

public class CommonsLangContainsDemo {

    public static void execute(String[] strings, String searchString) {
        if (ArrayUtils.contains(strings, searchString)) {
            System.out.println("contains.");
        } else {
            System.out.println("does not contain.");
        }
    }

    public static void main(String[] args) {
        execute(new String[] { "AA","BB","CC" }, "BB");
    }

}