Here is all of them: http://yoyowiki.org/wiki/Styles_Of_Play
Also known as 0A.
Loop based tricks with a single yo-yo. Zero A play consists of continuous loops, hops, and shoot the moons. Zero A is where most people start when they begin the style AA, and although Zero A is a relatively simple style, most people decide to practice A. Looping yo-yo’s usually are a modified or classic shape, and are usually weighted in the center. Those yo-yos used among popular players consist of the Yomega Raider and Fireball (usually modified), the YoYoJam Sunset Trajectory,the Duncan Speed Beetle, the Duncan Ballistic and the Relic, as well as many others from various other companies. No contest has been ever held for Zero A.
edit 1/2 A
This is a style of play where only one half of the yoyo is used. It was created by Joshua Yee in 1999 but has also been seen once done back in 2000 by Ryan Lai and in 2005 by Dave Poyzer This is a very difficult style and can only be performed with certain yoyos. (Yoyojams work best for this kind of trick).
Also known as single A and 1A.
String tricks with a single yo-yo. The yo-yo tends to be unresponsive (at advanced levels of play) to allow complicated string tricks to be performed.
Single A is what most people think of when you talk about yo-yoing. This style is also almost always the first style yo-yoers learn due to it being the most well known and the easiest to start.
1.5A is a sub-style within the 1A yoyoing class which utilizes by having the non throwhand have a tied string and the other hand to be the one which has the yo-yo. One goes ahead and does a normal throw and does 1a tricks, but then incorporates the string into play, cause a sort of extended amount of string. With this possibility, a number of tricks can be done that involves many mounts and maneuvers comparison to 3A. All together, it is like a sort of pseudo 3a but in itself, a completely different entity.
No one within the yo-yo community can correctly state who created 1.5a, and there has been many labels that have been swung around to identify it. What is known however is that Steve Brown and Mark McBride were doing such a style before 2001. Also such names as Daisuke Shimada and Peter West are players that represented it in a few clip videos of the past. The most common slang term for this is called “dual string”.
Most DS players will use two different string colours to represent the tricks involved since of its complex holds. They will also use different lengths of string to do different types of tricks, similar to players of regular 1a.
In the year 2007, this particular sub style has been revived from its long lost time, by such a players known by his internet screenname as “yblocyo” who then told a yo-yo friend which then made quite a number of videos depicting the style. the person that made these videos goes under the screenname “Magikai416”.
Also known as double A, 2A and two-handed yo-yoing
A style based on the use of two looping yo-yos, one in each hand. High-level AA play consists of various series of continuous regenerations, such as loops, hops, moons, punches, stalls, etc. Also performed are hundreds of different forms of around-the-worlds and other circular motions with the yo-yo. While combining loops and continuous circles, wraps can be done. Another growing part of AA (also possible in AAA) is based on the tangler trick, where the strings of the yo-yo cross, spin around the “knot”, and are then uncrossed.
Generally the yo-yos used for AA are based on either a modified or a classic shape. Those yo-yos used among popular players consist of the Yomega Raider and Fireball (usually modified), the YoYoJam Sunset Trajectory,the Duncan Speed Beetle,the Team Losi Da Bomb, the Duncan Ballistic and the Relic , as well as many others from various other companies.
Also known as triple A and 3A.
String (aka Long Spin) tricks with two yo-yos. Popularized and pioneered by Mark McBride, the first modern Triple A trick appeared in Fiend Magazine and was called Velvet Rolls. The different mounts are referred to as houses (e.g. “Kink House”).
Photos from as early as the late 1950’s show early yo-yo demonstrators performing very basic Triple A tricks, such as a Sleeper with one hand, and a Trapeze with the other. While Triple A as a concept has existed for many years, it was not until the release of Velvet Rolls that development began on what is currently considered Triple A.
Also known as OS and 4A.
Where the yo-yo is not attached to the string, but the string is tied to the finger. See the offstring article.
Also known as FH, counterweight and 5A.
Where a weight (typically a casino die or small ball) is attached to the end of the yo-yo string that would otherwise be attached to the finger. The yo-yo itself is attached to the string in the normal manner. Developed in 1999 by Steve Brown, freehand is considered to be the fastest-growing style of yo-yo play, as well as one of the most exciting to watch, due mainly to the wide diversity of styles from one 5A player to the next.
Manufacturing of a yo-yo with a fixed or sliding counterweight is covered under United States Patent #6,371,824.
edit Artistic Performance
Also known as AP
Artistic Performance is a style yo-yoing that uses any type of yo-yo or other prop in order to perform an artistic freestyle. This style is based mostly on performance of the player over the sheer number or complexity of tricks that they execute. Choreography, use of music, creative use of the stage, movement and performance is among the important aspects of this style of play. However yo-yo incorporation into said routines is a primary source of the performance.
edit Freehand Offstring
Also known as 9A (5A plus 4A), and offhand.
A counterweight is attached to the string, but the yo-yo is left unattached. This allows a great variety of tricks to be performed. Notable players of this style include Ryan Lai.
edit Sliding Counterweight
Also known as astro due to its similarity with the astrojax astrojax skill toy.
Originally called Astro Crap by its key innovator Seth Peterson due to the fact that few yo-yoers particularly like astrojax, but the name was later shorted to astro.
It is similar to freehand, but the counterweight is free to slide along the length of the string.
Conceived in 1999 by Chris Neff, Sliding Counterweight has gained popularity among freehand players in recent years due to the development of additional tricks and its mysterious “re-naming”, largely attributed to Seth Peterson and Doctor Popular. Both players are considered the pioneers of this style, as it was their tricks that have popularized it.
Invented by Steve Brown in early 1999, but also developed and popularized by Tommy Gun, this involves putting two yo-yos on one hand. Typically one goes on your ring finger, and the other on your pointer finger. This is to keep the yo-yos from hitting each other too much.
Tricks were shown in YoYoWorld Magazine issue #3 released winter of 1999. Tricks also appeared as single videos on his (old) site, as well as in Chicago Crew clip videos. Some tricks include Teamwork, Yellow Pages, Double Boing, Trapeze Entanglement, and Trapeze Traverser. While it has potential, this style really never caught on possibly because of the difficulty and aggravation of having less control over each yo-yo. AAA is quite similar so most people do that instead.
A style of play invented by Takahiko Hasegawa that involves two offstring yo-yos used simultaneously on a single string (although a second string is used for starting and finishing manoeuvres). A page describing this technique can be found here on YET.
Two yo-yos are attached at opposite ends of a single string.
The single string is modified so there is a normal loop at both ends instead of a loop at one and a slipknot at the other.
edit Doc Pop Style
Discussed on Radio Kwyjibo. Doctor Popular has developed many novel techniques, including using a paper-clip on the yo-yo end of the string while playing off-string. Using this light counterweight allowed him to return the yo-yo one-handed. This was done before the 1 handed whip-like regenerations developed by the Japanese offstring champion (Eiji?).
edit Loaf Style
Developed by John-Bot. It’s a style of one-handed yo-yoing mostly inside a gunslinger (split bottom) mount. It can best be described as one-handed tiny yo-yo tricks. The Boingy boingy is a probably the most well known trick from this style.
Invented by the Doctor Popular, it involves Single A tricks done inside the expanded slipknot loop of string that would usually go around your finger. The string is not attached to your finger. The style, also known as Moebius, is named after the theoretical physics concept known as a Moebius Loop.
As with any of the regular As, moebius can be done within those others as well and has been represented in various videos Within 2007 because of its revival. These other varaitions of moebius are called Triobius, Offbius, and Astrobius. Triobius utitlizes two yoyos that go with either slipknot to be opened and then do tricks ala to what 3a does. Offbius is when one opens the slipknot and hops it into there to then do tricks within it, while still the yoyo is technically offstring. Astrobius is where there is a counterweight attached at the end and then the slipknot is opened, which then the tricks done within the slipknot is then done similar to what Astro is like. That is where it got its idenity from.
A style recently shown by the Pretty Boy Spinners (PBS). Similar to freehand play, except that you throw the yo-yo and counter-weight in order to interact with your environment. Not recommended around living things.
This style was originally created by Chris Neff. Take a look at the Duncan How to be a Player Vol. 1 video.
edit Flying Eel
Also known as Slippery Eel or offhand.
This style is similar to freehand, but without the counterweight. Technique mostly involves using the weight of the yo-yo to bring the string around. Rarely done today.
It was popular among members of Team High Performance in 1998, and inadvertently led to the development of freehand by Steve Brown, due to his inability to successfully perform the Flying Eel tricks he was creating. The complicated nature of his creations necessitated some kind of stopper on the end of the string, and it was through experimentation with different beads and attachments that freehand was created.
This style was recently rejuvenated by CizreK, with his new video Free Floating. This video has developed quite a bit of controversy, because CizreK referred to it solely as “Free Floating,” as if it were a new style, even though the concept of the “Flying Eel” has been around longer than 5A. Although viewers of the video may be right, CizreK is one of the first players who has created useful and noteworthy “Flying Eel” tricks.
edit Washing Machine
Tricks performed by throwing the yo-yo as you would in A, but then unwinding the string and popping the yo-yo off the string. You then perform offstring style trick before putting the yo-yo back in the loop and returning it. Invented by Doctor Popular.
edit Double D
Also known as DD.
Double D is a combination of normal freehand and sliding counterweight, where you have two counterweights. One counterweight is tied to the string, the other is free to move. This style is quite similar to sliding counterweight, except the increased weight of the DD counterweight allows different maneuvers not possible with the typically light astro counterweights.
edit Double freehand
Also known as 13A (5A + 5A + 3A).
Double freehand is similar to AAA, but each yo-yo has a counterweight attached. It is a difficult style to do due to the fact there are four moving objects to worry about (two yo-yos and two counterweights). It was created by Steve Brown and originally named 13A, but it is sometimes referred to as 10A (5A + 5A). Notable players of this style include Rafael Matsunaga.
edit Go West
This is a style of play involving a fully untwisted string loop, much like a much larger version of washing machine. Tricks are created by maneuvering the yo-yo both while inside the string loop, and while off the loop, in a sort of pseudo offstring-1A style. Innovators of this style include Takahiko Hasegawa, Hironori Mii, and Kenji Nishi.
Invented by Doctor Popular around the same time the Japanese were innovating “Go West” style. Sumo stands for Super-Moebius and differs only in that you are playing with an regular yo-yo string that has just been completely untwisted. It differs from Go West because Go West is just a solid loop of string, with no finger knot, and Go West is usually double wrapped around the axle.
A style involving a sliding die as in Double D but the string is attached to the yoyoer’s finger. Invented by Vincent DeZutti.
Copied and pasted from that link.