Smith and Winston is a twin-stick shooter made entirely out of really small voxel blocks, it looks awesome and the destruction possible is also pretty amusing.
BulletRage is a game I firmly think is worth supporting, as the developer has had Linux support in very early and it does seem like a pretty awesome twin-stick shooter.
Originally developed for the 41st Ludum Dare Game Jam, ACardShooter is being expanded for a full release and it's due this Summer. Certainly sounds like an interesting idea too.
With a strange and unique visual style, Moss Destruction released back in March and while fun it was overly difficult at times. Recent updates are a dramatic improvement to the flow of it but it remains incredibly difficult.
Smith and Winston from Execution Unit is some of the most fun I've had in a twin-stick shooter for some time, partly because I love blowing things up and Smith and Winston lets you do a whole lot of that.
Moss Destruction from developer Shotgun with Glitters puts you up against various hordes of strange creatures, it recently left Early Access and I gave it plenty of time.
BulletRage, releasing later this year is a twin-stick shooter from Chimera One Games that promises non-stop action and I've had a play with a preview build.