The Horse stance is the most basic and widely taught stance in the world.
Its common definition is to have both legs equal.
Both legs are bent the about the same.
The feet are pointing the same angle in relation to the spine.
Both legs support the body weight equally.
Both legs generate the same type/amount of power.
The attacking power can be directed in all directions equally.
On top of all this, the horse stance can stop most throws and take downs merely by its maintenance. Try and find a throw which doesn't disrupt the stance as part of its first movement.
Many styles have variations on the horse stance which tend to be based on some specific use or concept. This basically means that a good horse stance can allow you to learn another style with minimal effort during the mental transition.
In addition, the horse stance is an earth stance. since all elements are created on the earth and are supported by the earth, It is believed that enough earth will balance all the other elements. This is why so many people teach the horse stance and say it does everything. Obviously there is a time requirement. For those of us who are not immortal, there are the other elements. Being earth, most applications in this stance involve absorbing or enduring as a defense. Offensively there is a lot of pounding and overwhelming, just like avalanches and landslides. Roundish (the earth is round), sloppy (like mud), hard (like stone), and continuous (the earth just goes on and on) tend to be the qualities of techniques in the horse stance.
Styles teach the horse stance first mainly because it allows the student to work with a minimum of confusion. Since power is equal in all directions, any major weaknesses can be covered with whatever strengths the student has. The student can work on the technique without worrying about what foot goes where. Visualizations tend to be easier since both legs are the same and the body does not shift much. It is a stance that can be done by nearly everyone and is the main posture for most chi kungs. In my personal experience I have found the horse stance in every art I have ever bothered to look at. Even people who say they don't train stances will usually be in one while they talk to you about it.