Does the "black panther" really exist? I read there are variations of black leopards, black jaguars and such but the animal we know as "black panther" is just a myth.

Black panthers (melanistic leopards) certainly exist, and they had an example in London zoo for some years. The reason for the melanism is not really known, and of course they stand out sufficiently well in the wild to be at a bit of a disadvantage when hunting - compared to a "normal" leopard. 

Closer examination** of the fur of a black panther show that they actually STILL have spots - different shades of black - in the fur.

**Closer examination is not advised in the wild. (Unless you wish to be mauled and eaten).