What is a good random number generator to use for a game in C++?
My considerations are:
Mersenne Twister is very good, and it's fast as well. I used it in a game and it's not hard at all to implement or use.
The WELL random algorithm was designed as an improvement over the Mersenne Twister. Game Gems 7 has more info. on it, if you can borrow that or have it.
On that WELL page I linked you to, the number is the period of the algorithm. That is, you can get 2^N - 1 numbers before it needs reseeding, where N is: 512, 1024, 19937, or 44497. Mersenne Twister has a period of N = 19937, or 2^19937 - 1. You'll see this is a very large number :)
The only other thing I can point out is that boost has a random library, which you should find useful.
In response to your edit, yes the Twister or WELL is that much better than rand(). Also, the old modulus trick harms the distribution of the numbers. Even more reason to use boost :)