Much of security relies on randomness - encryption keys should be random and random passwords are more secure than dictionary words or predictable sequences. The problem is, how do we generate a random number?
Well, actually, this is a trick question. The answer is that you can't generate random numbers, but you can observe them. Most programming languages give you a random number generator, so why not just use that? Well, it's not actually a random number generator, but a Pseudo-Random Number Generator (PRNG), or more accurately a Pseudo-Random Sequence Generator (PRSG). Given the same seed value, it will produce the same output every time. Try seeding the random number function in your favourite programming language then run your program a few times. You should see the same numbers coming out each time.
The reason for this is the function used to produce random numbers is just a mathematical formula that takes an input and gives an output. To have a random number out, you need a random starting value. Most will seed themselves on the clock, but this isn't random; it isn't even unpredictable. A simplistic example of a PRNG, as given by Knuth in his seminal books, is as follows:
X = (a*X+c) mod m
Random number = X/m for some suitable large prime number m and fixed values a and c both less than m (indeed c is usually a small number <10).
This can be seeded by setting X to the seed value and will give the same sequence of pseudo-random numbers out, as can be seen. However, it isn't random. If I know your seed value I can recreate your sequence of numbers. If you seed it on the clock it is often possible to work out a window of opportunity and obtain a range of seed values. Admittedly, this could be large, but an exhaustive search of these would be quicker than breaking the code that relies on them in many cases. Recently, a large Linux distribution was found to have a flaw in its key-generation that introduced a major weakness into the RSA public-key codes generated on those machines. This was due to predictability of the keys and a lack of randomness.
So, what can we do? We can observe randomness in the natural world. Random.org uses background white noise as a source of randomness. This gives good randomness and distribution of numbers. They offer several options to generate random numbers, sequences or even passwords. An example of their random number service is given below. I'm not saying that they are the best option or the only option, but you must use truly random numbers in your cryptography and secure systems.