"Wobbuffet does nothing but endure attacks - it won't attack on its own. However, it won't endure an attack on its tail. When that happens, the Pokémon will try to take the foe with it using Destiny Bond." - Wobbuffet's Pokédex entry from Pokémon Sapphire
This is a Pokémon that has almost little to nothing known about it. It learns no attacking moves other than Counter and Mirror Coat. These moves only work if the user is attacked first. It's "eyes" appear on it's tail. Also, according to the Pokédex entry, it does not tolerate when attacks are dealt to it's tail. This causes it to become angry and give it's foe the same fate as it has by using Destiny Bond.
What is this tail? A user by the name of "Bareiku" states,
"It is a key to another dimension. When another attacks or even touches it, it unlocks a separate world from ours. Using Destiny Bond, it drags the Pokemon assaulting its tail into it's realm and traps it there for all eternity, hiding it's secret, along with its assailant, before it's world could be seen and discovered."
As intriguing as this theory may be, it seems more of a guess than a theory. The truth behind the tail lies hidden between the lines of Wobbuffet's physical form and it's Pokédex entry.
Generation 5 Pokédex entries state:
"It desperately tries to keep its black tail hidden. It is said to be proof the tail hides a secret."
It has been widely discussed that Wobbuffet's tail is actually the controller of the form. Wynaut, Wobbuffet's pre-evolution, has a tail containing one eye, while Wobbuffet's tail has two eyes. The tail is black and the eyes are white with one black pupil. This is surprisingly similar to the eye of an Unown. Wobbuffet is also #202 in the National Pokédex, while Unown is #201.
Another user by the name, Sylveon88 came up with the theory:
"The Unown Report, when put in order, details some kind of "capturing" of another creature. It tells how the Unown chase down the creature, subdue it, and welcome it as one of their own. I think that Wobbuffet is a puppet to Unown. When a free Wobbuffet/Wynaut is discovered, the Unown take their bodies to protect themselves. This would explain Wobbuffet's Psychic-type. Wobbuffet have no direct damage-dealing moves, but Unown still send them off into the world without trying to protect the Wobbuffet when it is injured. If Unown cared about Wobbuffet, wouldn't it use Hidden Power to protect it? They just use Destiny Bond, showing that they don't care how hurt their host is."
Wobuffet was originally supposed to be an evolution to Unown. Most of Unown's Pokédex entries talk about a power that emerges whenever two or more of them interact. Wobbuffet is also one of the few Pokémon unable to learn the move Substitute. Wobbuffet is already the substitute, and has become the puppet of Unown's power. They use their Psychic powers to move their new body around and attack for them. This loosely explains Wobbuffet's Psychic-typing in the games.
The Unown don't mean any harm. That is why Wobbuffet has no first-strike moves. It also explains why Wobbuffet's tail has two eyes. Two Unowns created a powerhouse of a being that can withstand heavy blows and powerful attacks, only to dish them back with twice the power that was dealt. Even though they don't mean any harm, the Unown do not care about their host. This is where Bareiku was right, by saying,
"Using Destiny Bond, it drags the Pokemon assaulting it's tail into it's realm and traps it there for all eternity, hiding it's secret, along with it's assailant, before it's world could be seen and discovered."