How can I hash a password in Java?

You can actually use a facility built in to the Java runtime to do this. The SunJCE in Java 6 supports PBKDF2, which is a good algorithm to use for password hashing.

byte[] salt = new byte[16];
random.nextBytes(salt);
KeySpec spec = new PBEKeySpec("password".toCharArray(), salt, 65536, 128);
SecretKeyFactory f = SecretKeyFactory.getInstance("PBKDF2WithHmacSHA1");
byte[] hash = f.generateSecret(spec).getEncoded();
Base64.Encoder enc = Base64.getEncoder();
System.out.printf("salt: %s%n", enc.encodeToString(salt));
System.out.printf("hash: %s%n", enc.encodeToString(hash));

Here's a utility class that you can use for PBKDF2 password authentication:

import java.security.NoSuchAlgorithmException;
import java.security.SecureRandom;
import java.security.spec.InvalidKeySpecException;
import java.security.spec.KeySpec;
import java.util.Arrays;
import java.util.Base64;
import java.util.regex.Matcher;
import java.util.regex.Pattern;

import javax.crypto.SecretKeyFactory;
import javax.crypto.spec.PBEKeySpec;

/**
 * Hash passwords for storage, and test passwords against password tokens.
 * 
 * Instances of this class can be used concurrently by multiple threads.
 *  
 * @author erickson
 * @see <a href="http://stackoverflow.com/a/2861125/3474">StackOverflow</a>
 */
public final class PasswordAuthentication
{

  /**
   * Each token produced by this class uses this identifier as a prefix.
   */
  public static final String ID = "$31$";

  /**
   * The minimum recommended cost, used by default
   */
  public static final int DEFAULT_COST = 16;

  private static final String ALGORITHM = "PBKDF2WithHmacSHA1";

  private static final int SIZE = 128;

  private static final Pattern layout = Pattern.compile("\\$31\\$(\\d\\d?)\\$(.{43})");

  private final SecureRandom random;

  private final int cost;

  public PasswordAuthentication()
  {
    this(DEFAULT_COST);
  }

  /**
   * Create a password manager with a specified cost
   * 
   * @param cost the exponential computational cost of hashing a password, 0 to 30
   */
  public PasswordAuthentication(int cost)
  {
    iterations(cost); /* Validate cost */
    this.cost = cost;
    this.random = new SecureRandom();
  }

  private static int iterations(int cost)
  {
    if ((cost < 0) || (cost > 30))
      throw new IllegalArgumentException("cost: " + cost);
    return 1 << cost;
  }

  /**
   * Hash a password for storage.
   * 
   * @return a secure authentication token to be stored for later authentication 
   */
  public String hash(char[] password)
  {
    byte[] salt = new byte[SIZE / 8];
    random.nextBytes(salt);
    byte[] dk = pbkdf2(password, salt, 1 << cost);
    byte[] hash = new byte[salt.length + dk.length];
    System.arraycopy(salt, 0, hash, 0, salt.length);
    System.arraycopy(dk, 0, hash, salt.length, dk.length);
    Base64.Encoder enc = Base64.getUrlEncoder().withoutPadding();
    return ID + cost + '$' + enc.encodeToString(hash);
  }

  /**
   * Authenticate with a password and a stored password token.
   * 
   * @return true if the password and token match
   */
  public boolean authenticate(char[] password, String token)
  {
    Matcher m = layout.matcher(token);
    if (!m.matches())
      throw new IllegalArgumentException("Invalid token format");
    int iterations = iterations(Integer.parseInt(m.group(1)));
    byte[] hash = Base64.getUrlDecoder().decode(m.group(2));
    byte[] salt = Arrays.copyOfRange(hash, 0, SIZE / 8);
    byte[] check = pbkdf2(password, salt, iterations);
    int zero = 0;
    for (int idx = 0; idx < check.length; ++idx)
      zero |= hash[salt.length + idx] ^ check[idx];
    return zero == 0;
  }

  private static byte[] pbkdf2(char[] password, byte[] salt, int iterations)
  {
    KeySpec spec = new PBEKeySpec(password, salt, iterations, SIZE);
    try {
      SecretKeyFactory f = SecretKeyFactory.getInstance(ALGORITHM);
      return f.generateSecret(spec).getEncoded();
    }
    catch (NoSuchAlgorithmException ex) {
      throw new IllegalStateException("Missing algorithm: " + ALGORITHM, ex);
    }
    catch (InvalidKeySpecException ex) {
      throw new IllegalStateException("Invalid SecretKeyFactory", ex);
    }
  }

  /**
   * Hash a password in an immutable {@code String}. 
   * 
   * <p>Passwords should be stored in a {@code char[]} so that it can be filled 
   * with zeros after use instead of lingering on the heap and elsewhere.
   * 
   * @deprecated Use {@link #hash(char[])} instead
   */
  @Deprecated
  public String hash(String password)
  {
    return hash(password.toCharArray());
  }

  /**
   * Authenticate with a password in an immutable {@code String} and a stored 
   * password token. 
   * 
   * @deprecated Use {@link #authenticate(char[],String)} instead.
   * @see #hash(String)
   */
  @Deprecated
  public boolean authenticate(String password, String token)
  {
    return authenticate(password.toCharArray(), token);
  }

}

BCrypt is a very good library, and there is a Java port of it.