In the 21st century, a lift Amy Pond and Rory Williams had just entered, at the apartment building of a boy named George, instead of going up, shot down at an alarming rate. They regained consciousness in George's cupboard doll house, and immediately assumed they had died from the fall.
At a later date, hospital orderlies captured Rory Williams and his father Brian in a wormhole portal disguised as a disused hospital lift. The Eleventh Doctor and Amy later discovered the portal in the lift, and confronted a Shakri on the other side. (TV: The Power of Three)
A lift in Sanderson & Grainger was out of order in 2011, and also used as a portal; this time, it was a link made by the Cybermen to their Cyber-ship. When the Eleventh Doctor and Craig Owens first entered it, they were almost attacked by Cybermen. The Doctor did his best to keep Craig distracted, so he wouldn't look around, even almost kissing him. (TV: Closing Time)
Also in the 21st century, Mel and Pex used a lift in Paradise Towers to try to get to floor 304. However, the cleaners overrode the controls and had the lift alternate between floors 173 and 174. Pex kicked the controls and the lift plummeted to the basement. There, they managed to get it working again and made it to floor 304. (TV: Paradise Towers)
The lifts inside Kaalann on Skaro were broken down before the Daleks returned to the planet with the Eye of Time and rebuilt their race. This was undone when the Eleventh Doctor and Amy travelled through the Eye and stopped the Daleks before they could harness the Eye. (GAME: City of the Daleks)