Java 6 :

this is how I did it using javax.xml.bind.DatatypeConverter - this works from at least Java 6 on:

import java.io.UnsupportedEncodingException;    
import javax.xml.bind.DatatypeConverter;

public class EncodeString64 {

    public static void main(String[] args) throws UnsupportedEncodingException {

        String str = "77+9x6s=";
        // encode data using BASE64
        String encoded = DatatypeConverter.printBase64Binary(str.getBytes());
        System.out.println("encoded value is \t" + encoded);

        // Decode data 
        String decoded = new String(DatatypeConverter.parseBase64Binary(encoded));
        System.out.println("decoded value is \t" + decoded);

        System.out.println("original value is \t" + str);

    }

}

Java 8:

Java 8 now supports BASE64 Encoding and Decoding. You can use the following classes: java.util.Base64, java.util.Base64.Encoder and java.util.Base64.Decoder.

Example usage:

// encode with padding
String encoded = Base64.getEncoder().encodeToString(someByteArray);

// encode without padding
String encoded = Base64.getEncoder().withoutPadding().encodeToString(someByteArray);

// decode a String
byte [] barr = Base64.getDecoder().decode(encoded);