The Luhn algorithm is often used for credit card number validation. The code below gives an explanation in its comments as to how it works, but further description can be found here. The source is downloadable HERE

public class Luhn {
public static boolean check(String ccNumber) {
// How many digits should there be - perhaps it can vary? Anyway should be all digits
if (!ccNumber.matches("\\d+")) {
throw new RuntimeException(String.format(
"CC number %s should be all digits", ccNumber));
}

// Keep running total
int sum = 0;

// 'odd' in the sense of an undefined index, starting at 0
// so the first odd character will be the second one we look at (index 1)
boolean odd = false;

// Start inspecting each digit from right to left
for (int i = ccNumber.length(); --i >= 0;) {
int n = ccNumber.charAt(i) - '0';

if (odd) {
// Double each alternate digit
n *= 2;

// If result of doubling in two figures, make it one figure
// which is the sum of the two digits
if (n > 9) {
n -= 9;
}
}

// Accumulate
sum += n;
odd = !odd;
}

//Accumulated total should be multiple of 10
return ((sum % 10) == 0);
}

public static void main(String[] args) {
System.out.println(Luhn.check(args));
}
}