Ultima Tower from Stephen Baxter's novel Flood. It is located in Manhattan in the flooded world of the novel's setting. It is described as being 10 miles or over 16 km tall, consisting of 960 levels.
Some other examples -
The Mile High Tower in the Judge Dredd comics - Exact height varies but has been depicted from 1 mile up to 2.5 miles tall (1.6 - 4 km). Serves as part of the vast cityscape of Mega-City One.
Trantor in Isaac Asimov's Foundation series - The capital planet of the Galactic Empire featured a continuous mass of metal constructed thousands of stories tall covering the entire surface of the planet.
Babylon 5 space station in the TV series of the same name - The cylindrical station is 10 miles tall (16 km) and houses 250,000 inhabitants. Not a planet-based structure but shows the epic scale possible in sci-fi construction.
Imperial Palace on Coruscant in Star Wars - The restored palace of Emperor Palpatine towered over surrounding skyscrapers, with a height of several kilometers up to 5 km claimed in some sources.
Ziggurat in Peter Hamilton's The Naked God - A massive stepped pyramidal tower reaching up from an enclosed planet, about 5 km tall with 500 levels.