The latest DC Universe Online update added support for cross-platform play between PC, PlayStation 3 and PlayStation 4.
As of now, DC Universe Online players from PC, PS3 and PS4 can play together on the same servers "in groups, in leagues, in On Duty content, and in the open world." Keep in mind that the player accounts are still locked to their respective platforms, so you can't transfer your characters or purchases from your PC account to your PS account or vice versa.
The transition has already occurred seamlessly with the only noticeable change to users being an increased number of players around them.
DC Universe Online is a free-to-play massively multiplayer online action game set in the DC Comics Universe. It was released on January 11th, 2011 and it currently enjoys a MetaCritic score of 75. By the end of 2014, the game had 18 million registered users, and is the number one revenue generating free-to-play title on the PlayStation 3 and 4.
An Xbox One version of DC Universe Online is in production for a spring release. There is no word yet on whether this version will support cross-play with the existing versions.