Here are some frequently asked quesitions. Many of them are to the older version (1998-99 versions). The 2002-version MT19337ar.c(2002/1/26) addresses to these problems.
• ### Want half-open interval[0,1). More precision than 32-bit.

2002-version mt19937ar.c has versions [0,1],[0,1),[0,1),(0,1) (32-bit precision), and [0,1) with 53-bit precision.
• ### Want more precision.

One may concatinate two output words, to obtain 64-bit integers.
• ### Want to use for cryptography.

Mersenne Twister is not cryptographically secure. (MT is based on a linear recursion. Any pseudorandom number sequence generated by a linear recursion is insecure, since from sufficiently long subsequence of the outputs, one can predict the rest of the outputs.)

To make it secure, you need to use some Secure Hashing Algorithm with MT. For example, you may gather every eight words of outputs, and compress them into one word (thus the length of the output sequence is 1/8 of the original one).

It is meaningful to replace linear generators like LFSR with MT.

2002-version can receive an array of integer as a seed, and it fits to this usage.
• ### Want a larger space for the seed than 32 bits.

2002-version mt19937ar.c has two initialization schemes: (1) init_genrand(seed), receives one unsigned integer, (2) init_by_array, receives an array of unsigned integers and its length. This enables us to use an array of arbitrary length, as a seed.
• ### Want a uniform random number in the integers [0..N-1].

If N is not large (say, <216) and you don't need the precision, it would be enough to use [0,1)-version (use double-precision), multiply the output by N, then take floor (round-off). (Caution: do not use [0,1]-version. Appearance of 1.0 may cause the output of N. This occurs roughly once in 4.2 billion times).
WARNING: this solution has numerical error in the distribution, unless N is a power of 2. The order of the error is N times 2-32. A better, safer method is to obtain minimum integer n such that N<=2n, generate integer random numbers, take the most significant n bits, and discard those more than or equal to N.
• ### Want to save the state, and later continue the generation.

In the case of mt19937ar.c, if one saves mt[N] (624 words) and the counter mti (1 word), then one can continue the computation by loading these values.
There are a few versions supporting these functions of "save/store the state." See Mersenne Twister in C, C++ in particular the implementation by Richard Wagner.