When services like Xbox Live and PlayStation Network experience significant outages and/or connection problems, it has become typical for them to offer users one or more free games as an apology.
Virtua Fighter - September 1995
The very first consolation game could be said to be Virtua Fighter Remix. When the initial Saturn version of Virtua Fighter was released for the platform in May of 1995 many players noticed that the game looked and played significantly worse than the arcade version. Sega agreed with them and, by September, released an updated version that fixed most of the complaints about the game. In a show of good faith, Sega sent out a copy of the newly christened Virtua Fighter Remix, to anyone who purchased the original.
Xbox Live - Christmas 2007
Presumably due to the influx of new users immediately following the 2007 holiday season, Xbox Live experienced several days of connection issues that kept many players from playing all those new games they had received as gifts. As an apology, Microsoft offered all gold members a free copy of Undertow, which could be downloaded between January 23 and January 27, 2008.
PSN Outage 2011
After an "external intrusion" compromised over seventy million users' account information, Sony was forced to shut down PlayStation Network on April 20, 2011. The service remained down until May 15, 2011. Following the outage, Sony launched the "Welcome Back" program, which offered one free month of PlayStation Plus and two free games to PlayStation 3 and PlayStation Portable owners available for download for thirty days after the outage. Those who owned both systems were able to select two games for each.