Raj's Apartment, 3D, or the Raj Mahal, is where Raj lives. It is a small apartment, with one bedroom, in a 67-year-old building (built 1951) that used to be a watch factory (in "The Bad Fish Paradigm", Sheldon worries about the residual radium from the manufacture of luminous dials).
Priya Koothrappali (Raj's younger sister) stayed here when she was visiting and dating Leonard. Leonard even moved in switching places with Raj when it looked this he and Priya were going to move in together. She announced she was going back to India by the end of the episode.
Penny has been there twice: once at the end of their "date" and once after she drops Leonard off at the airport to check on Raj.
In season 10, Raj evicted himself out his apartment in The Escape Hatch Identification. After he cut himself off his from parent's financial supply in The Allowance Evaporation, he is now unable to afford to live there anymore and his salary from Caltech is not helping him with it due to his other expenses.
Rajesh Koothrappali's apartment is featured in many episodes:
The Bad Fish Paradigm - Sheldon stays with Raj briefly, until Sheldon unintentionally offends Raj by comparing the Bollywood dancer Aishwarya Rai to Madhuri Dixit, leading Raj to kick him out to Howard's house.
The Griffin Equivalency - Raj returns with Penny still drunk where he speaks to his parents, before leaving to the bathroom to throw up.
The Cornhusker Vortex - Howard tries to make up with Raj after he ditched him for an attractive woman.
The Guitarist Amplification - Raj argues with his parents, when Sheldon is about to stay at his place, but leaves at the last minute.
Season 4 - Appears most frequently during this season when Raj's sister, Priya is in town and starts dating Leonard. This causes Raj to stay with Sheldon in the season's last episode, until Priya's relationship is found out and she goes back to India.
The Monster Isolation - Raj becomes depressed when Lucy abandoned him and he stays in his apartment in solitude.
The Closure Alternative - Raj has a date with Lucy.
The Bon Voyage Reaction - Lucy and Raj have dinner with Amy. Penny later comes over to comfort him and he realizes that the breakup somehow broke him free of his selective mutism towards women (Raj didn't drink alcohol after the breakup).