The Wailing Caverns in the Barrens is one of the first instanced dungeons (outside of a major city) that lower-level Horde players encounter. It is also worthwhile for Alliance characters to run, though possibly inconvenient, as it is located in Horde territory.
This instance is extremely conducive to solo play for characters of most classes after around level 30 to 35. At these levels one will be all but immune to some of the more troublesome effects, such as the Druids of the Fang's sleep spell. Those under level 40 should exercise caution when pulling mobs.