The random number generators you find on computer systems are actually “pseudo” random number generators. The values appear to be random but are created from a deterministic algorithm. Random.org, however, has a truly random generator which uses atmospheric noise as the randomizer. And you can automatically retrieve numbers via the web using HTTP GET requests like this one.
Another such effort, the Quantum Random Bit Generator Service, uses quantum effects to achieve randomness. They don’t currently have a web service interface, however, and to access the random data you’d need to include their libraries in your code.
Thanks to Josh for this topic.