Mersenne Twister is a non-cryptographic RNG that's commonly used in many applications. According to Wikipedia:
The Mersenne Twister is the default PRNG for the following software systems:
Microsoft Visual C++, Microsoft Excel, GAUSS, GLib, GNU Multiple Precision Arithmetic Library, GNU Octave, GNU Scientific Library, gretl, IDL, Julia, CMU Common Lisp, Embeddable Common Lisp, Steel Bank Common Lisp, Maple, MATLAB, Free Pascal, PHP, Python, R, Ruby, SageMath, Scilab, Stata. It is also available in Apache Commons, in standard C++ (since C++11), and in Mathematica. Add-on implementations are provided in many program libraries, including the Boost C++ Libraries, the CUDA Library, and the NAG Numerical Library.
Mersenne Twister is a very good PRNG, with good statistical properties, very long period, and is fast. Despite being a very good PRNG, and is widely used for many games, statistical simulations, and other purposes, it's not suitable for cryptography.
Another common RNG is linear congruential generator (LCG), which for a long time is the default RNG in popular C libraries (and many other languages that uses C library, such as PHP). LCG is a simple but very poor RNG, even for non-cryptographic RNG standards. Its period size is embarrassingly small, already-produced numbers cannot repeat for the entire period, and it has statistical properties that makes it unsuitable for many purposes.