Starmancer, a space station sim inspired by Dwarf Fortress currently on Kickstarter will have full Linux support, even during alpha and beta. It looks damn good too!
Pixeljam are currently crowdfunding Dino Run 2, their next fast-paced dinosaur themed platformer. I had some concerns about their Linux support, so I got a few questions answered.
KING Art, developer of The Dwarves and The Book of Unwritten Tales are considering Kickstarter for their new RTS 'Iron Harvest' and they need feedback from a survey, with Linux as a platform option.
Lingotopia looks pretty interesting, a language learning game about being lost in a city. It's on Kickstarter and it's fully funded with Linux support confirmed.
Few games make me excited beyond help, especially when they're on Kickstarter, but space drone building game Nimbatus is fully funded and coming to Linux. I tested it and I love it.
This fully-voice-acted point and click/visual novel hybrid is currently looking for crowdfunding to be completed. A short prologue demo is available to try it out.
Desert Child caught my eye today as the whole idea sounds pretty awesome and I do love racing games, it mixes in some RPG mechanics too and plenty of action.
Top-down spaceship simulator 'Shortest Trip to Earth' inspired by FTL and Firefly is now on IndieGoGo and it has a Linux demo. I've tested it and loved it.
The Untold Legacy is a story-rich action adventure game, with hack and slash gameplay and a little sprinkle of RPG elements it promises to be quite an interesting title.