• ThreadLocalRandom, the recommended and most modern class (from Java 7)
• SecureRandom, a cryptographically strong random number generator
• Random, the superclass of both ThreadLocalRandom and SecureRandom
• Math.random, a static method which generates doubles evenly distributed between 0 (inclusive) and 1 (exclusive).

To generate a series of random numbers as a unit, you need to use a single object. Do not create a new object for each new random number.

When methods in these classes accept a lower and upper bound, the lower bound is inclusive and the upper bound is exclusive.

Example

import java.util.concurrent.ThreadLocalRandom;

/** 
 Generating random numbers with ThreadLocalRandom.
 In Effective Java, Joshua Bloch recommends ThreadLocalRandom 
 for most use cases (even for single-threaded code).
 
 @since Java 7.
*/
public final class RandomNumbers {
  
  public static final void main(String... args){
    RandomNumbers prng = new RandomNumbers();
    prng.zeroToUpperBound(100);
    prng.range(10, 21);
    prng.gaussian(100.0, 5.0);
    log("Done.");
  }
  
  /** The upper bound is excluded. */
  void zeroToUpperBound(long upper){
    log("Generating " + MAX + " random integers in the range 0.." + (upper-1));
    //a single object is reused here
    ThreadLocalRandom generator = ThreadLocalRandom.current();
    for (int idx = 1; idx <= MAX; ++idx){
      long random = generator.nextLong(upper); 
      log(INDENT + random);
    }
  }
  
  /** The lower bound is included, but the upper bound is excluded. */
  void range(long lower, long upper){
    log(
      "Generating " + MAX + " random integers in the range " + 
      lower + ".." + (upper-1)
    );
    //note the static factory method for getting an object; there's no constructor, 
    //and there's no need to pass a seed
    ThreadLocalRandom generator = ThreadLocalRandom.current();
    for (int idx = 1; idx <= MAX; ++idx){
      long random = generator.nextLong(lower, upper); 
      log(INDENT + random);
    }
  }
  
  void gaussian(double mean, double variance){
    log("Generating " + MAX + " random doubles in a gaussian distribution.");
    log("Mean: " + mean + " Variance:" + variance);
    ThreadLocalRandom generator = ThreadLocalRandom.current();
    for (int idx = 1; idx <= MAX; ++idx){
      double random = mean + generator.nextGaussian() * variance;
      log(INDENT + random);
    }
  }
  
  //PRIVATE
  private static final int MAX = 10;
  private static final String INDENT = "  ";
  
  private static void log(String aMessage){
    System.out.println(aMessage);
  }
}
 

Generating 10 random integers in the range 0..99
  4
  71
  31
  88
  95
  69
  94
  24
  36
  39
Generating 10 random integers in the range 10..20
  18
  11
  15
  17
  11
  10
  12
  19
  16
  15
Generating 10 random doubles in a gaussian distribution.
Mean: 100.0 Variance:5.0
  96.29657359305843
  99.72442335141267
  103.91992986911049
  96.53271254805549
  101.20312372014465
  102.12709319015893
  103.7626473084215
  102.47094971891569
  100.86789127025881
  101.78107900928805
Done.