3x3x3 Rubik's cube: the most commonly used speedcubing methods
There are typically several possible ways to solve a specific problem. The 3x3x3 Rubik's cube is no exception in that. One can use a couple of methods in order to get a solved state from a state of utter chaos.
If we ignore cheating (relabeling and peeling off the stickers, disassembling of a cube to individual cubies etc.), existing methods may be divided into groups by several criteria. Whether by a number of needed moves, solving principle, number of needed algorithms, or last but not least by a popularity among cubers. The term "speed of method" hasn't been deliberately mentioned because it is misleading at least. The method itself can't be "fast", unlike the speed of execution of speedcuber's moves, case recognition (cube state) speed or speed of rotation of used cube. Following video shows that if these factors are well-balanced, almost any method can be "fast".
Basic 3x3x3 Rubik's cube solving methods, which are most widespread among speedcubers (although frankly, I'm not aware of anyone who would use either ZB or Heise as his/her main method), are presented below.
On this page you will find the following methods:
CFOP / Fridrich
CFOP (Cross, F2L, OLL, PLL) is a method proposed by several cubers in the 80's of the twentieth century. It is also known as the Fridrich method after its popularizer, Jessica Fridrich. Partially due to her method publication on the internet in 1997, CFOP (and its variants) has been the most dominant 3x3x3 speedcubing method since 2000, used by the vast majority of speedcubers. Until recently, every speedcuber ranked in the top 10 by 3x3x3 average has been using CFOP (or its variant).
This method is relatively easy to understand in comparison with other methods. Therefore, it is the most tested and popular one. It has a reasonable number of algorithms, and sub 15 second averages are definitely possible with it. This method has been used to set many world records. It takes less thinking than block-building methods because it's more algorithm-based.
Learning all of the algorithms takes some time, and it requires a lot of practice to solve F2L consistently in 10 seconds or less. Also, it has a slightly higher move count when compared to block-building methods.
Frenchman Gilles Roux is the author of the Roux method, he described it in 2003. Solving process is similar to a combination of the Petrus method's block-building and the Waterman method, which is a representative of corners-first methods.
The Roux method uses fewer moves than the popular CFOP. It is also more intuitive and requires fewer algorithms. After the first block is built, the rest of the cube can be solved mostly with R, r M and U moves, thus eliminating cube rotations.
Block-building can be tough for beginners to get used to. Execution of M and r moves may also be difficult for some people. Cubers who have trouble with M moves should probably not use this as their main method (or better, practice practice practice the M moves). Two-layer moves (e.g. r move) can also be slower than using a quarter-turn metric moves (R move, for example).
Zbigniew Zborowski from Poland is the author of the ZZ method. He described it in 2006. The method is focused both on low move count and high turning speed.
For F2L, no cube rotations are required and only R, U and L moves are needed. Pre-orientation of edges halves the F2L cases and makes edges easier to find and connect to blocks/corners. The cube is typically held in the same orientation throughout the solve which allows to trace "locations", allowing fast/intuitive placing of cubies without thinking/looking. With a block-building-based F2L and pre-orientation of last layer edges, around 55 moves can be achieved without difficulty (to solve the cube). Optimization of F2L block-building and adoption of more advanced last layer systems will reduce move count significantly. Intuitive block-building during F2L is fairly easy to pick up and only 20 algorithms (assuming mirror cases) are required to solve the last layer in two looks. With edges being pre-oriented, many techniques exist for completing the last layer.
ZZ is heavily influenced by inspection time. It is fine when 15 seconds are given, however, in situations where no inspection time is used, it can be a drawback. For example, when using reduction on bigger cubes than 3x3x3 or within multi-solve scenarios, ZZ solve can be difficult (for speed) to handle. EOLine is hard to plan and execute in one step and takes a long time to master. Beginners should expect it to take in the order of months to achieve full EOLine inspection in 15 seconds. F2L in ZZ requires to solve two more cubies (10 in total) than in CFOP (8 in total).
Lars Petrus from Sweden is the author of the Petrus method. He described it in the 80's of the twentieth century. This method deals with a gradual building of blocks.
The Petrus method uses fewer moves than CFOP and most of other non-block-building methods. It is more intuitive than CFOP, and requires far less algorithms. Using some techniques, you can orient and permute the corners at the same time. The last layer can be even solved in one look, however, it drastically increases the number of algorithms you must learn.
Especially for beginners it can be hard to optimize block-building. It's also difficult to keep consistently turning without major time delays throughout the solve.
The authors of the ZB method are Zbigniew Zborowski from Poland and Ron van Bruchem from the Netherlands. They described it in 2002. Similarly to CFOP, it is an advanced variant of layer-by-layer solving method (LBL).
After solving F2L minus one edge-corner pair, there are just two more steps to solve the whole cube (finishing of F2L with simultaneous orientation of edges of the last layer, and finishing of the last layer in one algorithm). Zbigniew Zborowski claims that the method requires only 40 moves on average.
The method has a total of 300 algorithms (for F2L), or just nearly 800 overall algorithms. It takes a very long time to learn the entire method.
The author of the Heise method is Australian Ryan Heise, who described it in 2003. It is an intuitive method requiring no algorithms and using extremely few moves, but it may be difficult to get good times with it.
Usage of the working corner & working edge technique can be perceived as a beginner's version of the Heise method.
The method is more efficient than most (if not all) of the other methods described here, and is therefore very suitable for fewest moves solving. Since there are no algorithms, cubers using this method generally become very good at intuitive block-building. They also develop a high-level theory / understanding of the cube.
Every turn has to be planned out, so fast turners will be disappointed. Some of the steps can be very difficult to get used to, and beginning cubers might not sufficiently understand cube theory which is needed for this method.
References (links valid as of February 25, 2013):
The page was graphically improved by Michael Feather.