Square Enix has announced that the beta of Final Fantasy XIV: A Realm Reborn has managed to top the previous record of concurrent users for an open beta.
A few days ago, Director Yoshida tweeted that the FFXIV servers were undergoing stress due to 120,000 concurrent users playing, and because of this, Square Enix had to add two additional servers. (Typhoon and Ultima)
24 hours later, Square Enix announced that they had broken the record again, this time by having 150,000 concurrent users.
The previous record was held by Phantasy Star Online 2 that saw 107,000 people online at the same time on July 24th, 2013.
Update: Now that the game has launched, it has once again broken the record for the most users online at the same time by reaching over 200,000 concurrent users online at the same time! The servers are getting upgraded September 3, 2013 (starting at 5 AM PDT, lasting 10 hours) to fix the log in problems people have been having as well.
Check out this article from DualShockers for more information about the latest record.