Dancing

You can command your character to dance when you use the following slash command:

Each gender of each race has a different style of dance. Appropriate music is not provided. New dance cycles were originally announced for the release of the second expansion, Wrath of the Lich King, and are still being advertised as a new feature thereof on their official website.

Here is the official statement from Blizzard:

Alliance races

 * Worgen in their human forms will do the human dance animations instead.

Allied races
As the allied races use the framework of other core races, the Dark Iron dwarves, Mag'har orcs, Highmountain tauren, nightborne, void elves, and Lightforged draenei share the dances of the races they are based on. In the case of the Mechagnomes and vulpera, they take inspiration from the same sources; with the Mechagnome dances being flipped by gender, while the vulpera are different sections of the same dance.

Dance animations and videos
Blizzard released a webpage where you can view (and download animated images of) the dances performed by the WoW Classic races: However, the animations on the site do not show the entire set of dance moves.

You can also view dance-mixes with models and real movie-clips: WoW dance mix on Youtube

For a compilation of all the playable classes, plus races like ogres, go to Wow dances (strangely excluding dwarves)