Ratchet & Clank (possibly start with R&C Future Series and the new PS4 game). One idea may be to make the badge a play on the Grummelnet style of images of Ratchet:
The other possibility for Ratchet & Clank would be a badge of the Rhino weapon. Since the Rhino has a different appearance in each game, they would be distinct enough to visually describe the game at a glance.
Amanita Games series, primarily Samorost 1-3, and Machanarium.
The Team Ico trilogy: Ico, Shadow of the Colossus and The Last Guardian
Limbo and Inside
Portal 1 & 2
Chrono Trigger (defintely an image of the Epoch)
Far Cry 3: Blood Dragon (Title: Rex “Power” Colt)
Monkey Island series
Silent Hill 2-4 (possibly more eventually)
Doom, Doom 2, Doom 2016