Parallel universe

A parallel universe was a reality created when historical events diverged from the main timeline. Unlike alternate timelines, these occurred naturally. Travel to parallel universes became impossible after the Last Great Time War. (DW: Rise of the Cybermen)

History
In the 1970s, the Third Doctor visited a parallel universe in which the United Kingdom was a fascist Republic ruled by an alternate Doctor. (DW: Inferno, NA: Timewyrm: Revelation)

Circa 1979, the Fourth Doctor visited a universe in which the Roman Empire spanned the galaxy and was beginning to conquer other universes. (DWM: The Iron Legion)

One parallel universe was lifeless and empty due to the destruction of Logopolis in 1981. (PDA: The Quantum Archangel)

In the 1990s, Carbury was invaded by knights from a parallel universe which bore similarities to Arthurian legend. (DW: Battlefield)

In 2007, the Tenth Doctor, Rose Tyler and Mickey Smith visited a universe in which Rose's father was still alive. (DW: Rise of the Cybermen)

In 2008, Ianto Jones accepted the offer of Mairwyn. He did not die when the 456 invaded and Mairwyn enslaved Earth. The two later visited the "real" universe to observe Ianto's funeral. (TM: Shrouded)

A parallel universe, where Earth was part of a meta-government called the United Federation of Planets, was joined with the Doctor's at one point, resulting in the Fourth Doctor coming in contact with the Federation in the 23rd century and the Eleventh Doctor in the 24th century. (IDW: Assimilation²)

In one parallel universe, the Ironsides were used to end World War II some years early, then were destroyed. (DWAN: Doctor Who The Official Annual 2011)