Friedrich and Petrus methods are quite common, as well as the Roux method. Some other methods are Heise, Zbroski-Brucem, and Vandebergh-Harris. Several of the beginner cubers use the Beginner Method.
CFOP/Friedrich[]
The Friedrich Method, sometimes called CFOP, was invented by Jessica Friedrich. It has 4 steps: Cross, First two layers (F2L), Orienting Last Layer (OLL), and Permuting Last Layer (PLL). There are many algorithms. Almost all the top speedcubers use CFOP/Friedrich. These cubers include Max Park, Feliks Zemdegs, Yusheng Du and many more.
Roux[]
The Roux Method was invented by Gilles Roux. It has 4 steps, a 1x2x3 block, another one on the opposite side (F2B), orienting and permuting last four corners (can be done in one step called CxLL, as COLL, CELL... all work, even if CMLL are the best ones) and finally the last six edges (L6E or LSE), where you orient and permute the last remaining edges and finish the cube.
Zbigniew Zborowski[]
The ZZ Method or the Zbigniew Zborowski Method is a method for speedsolving the cube created in 2006. It has many different variations.
Beginner[]
The Beginner Method is a very slow method with the highest solve speed possible being about 22-25 seconds. This is a common method among beginners, therefore, it is called Beginner Method. It consist of solving the first layer (cross,corners), second layer (edges), and final layer(cross, correct colored cross, corners, corner alignment).