Random algorithm with biggest sequence that never repeats

I am going to attempt to write a random number generator using exisiting randomize algorithms. Can you suggest which algorithm has the biggest sequence that never repeats? I don't care if they are fast or slow.

If you don't want to follow Yuval's advice :), Mersenne Twister algorithm is a good random number generator and has a quite simple implementation (period of $2^{19937}−1$). See Wikipedia page for quick highlights on advantages/disadvantages. There are also many open source implementations in many programming languages.

For technical details and in-deep analysis of the algorithm see M. Matsumoto's articles that are available on his page.

StackExchange Computer Science Q#3421, answer score: 6