Alternate counterparts of Donna Noble existed in other realities. These individuals shared similarities with Donna from the Doctor's universe, despite existing in parallel universes or alternate timelines.
In at least one reality, Donna Noble didn't exist. Sibling Same and Sibling Different once visited a timeline in which Donna never existed. (PROSE: The Paradox Moon)
Parallel Worlds
Donna's World
Donna Noble was coerced by the Trickster's Brigade into turning right instead of left on 25 June 2007; this small change in affairs produced Donna's World. In this world, Donna never met the Doctor, and so - without her intervention - the Tenth Doctor died in his confrontation with the Empress of the Racnoss.
With the help of Rose Tyler, Donna forced her younger self to turn left instead of right, negating her world. The original Donna later displayed knowledge of the events of this timeline. (TV: Turn Left)
Rob Tyler's universe
In one parallel universe, Donna Noble was a contact of the Agency. She had seemed to cease all contact when she managed to infiltrate a top-secret satellite base. (AUDIO: The Flood)
The Daft Dimension
to be added
Rogue planet's universe
In another parallel universe, Donna Noble foretold the end of the world via a prophecy known as the prophecy of the three comets. According to her, a woman calling herself Bad Wolf warned her that the stars were going out. Rose guessed that she might find Donna on another universe and warn her about the three comets, which would eventually bleed into this Donna's subconscious. (AUDIO: The Rogue Planet)