A RandomNumberGenerator is either a piece of hardware or software that generates random numbers in the widest sense. There are many different approaches, however, the biggest distinction is between true random number and pseudorandom number generators.

A good RandomNumberGenerator is crucial to applications in Cryptography: if an attacker can guess the sequence of "random" numbers used to generate keys or other variables for your algorithm, he gets an important foot in the door for cracking your communication -- or can even walk right in.

True random number generators

These must be hardware. A variety of approaches for their design exist, but listening to white noise or radioactive decay seem to be the most popular ones. There are a number of publicly queriable true random number generators on the web, such as http://www.random.org/ and http://www.fourmilab.ch/hotbits/.

Pseudorandom number generators

A pseudo random number generator such as offered by the random(3) and rand(3) of the C standard library generates numbers using mathematical algorithms. Such a generator has a "period", which means that it produces a repeating sequence of numbers. With a good algorithm, the period length can well reach billions of numbers.

However, this is difficult terrain and requires thorough understanding of statistics and very sharp math skills. Do not attempt to roll your own. Most naive attempts at handrolled pseudorandom number generators have alarmingly short period lengths. Often, hapless programmers will lump together two different algorithms with decent period lengths each to get an "improved" one -- which usually results in a generator with a shorter period!

Note that true randomness is not always desirable. Random number sequences often have certain specific characteristics which make them better suited as input to certain kinds of statistical algorithm, because they cause a far faster convergence toward the same final result than truly random numbers could. Truly random numbers also make debugging much harder for obvious reasons; if you want to verify an algorithm, you want to be able to replay number sequences as necessary. On the other hand, you will usually need a statistically decently random sequence to examine the longterm behaviour of the algorithm.

So there are many areas where pseudorandom numbers are actually more desirable than truly random ones.

Hybrids

In Unix systems, there's commonly a /dev/random device to access a pseudorandom number generator. This generator however includes a twist that lets it generate higher quality random numbers than otherwise expected: its seed is periodically perturbed using using low-level timing information from the network, mouse, keyboard, and possibly other entropy sources, which only the Kernel has proper access to. It is generally considered a sufficiently good generator for everything except the random numbers to be used in cryptographic suituations PublicKey generation.