They don't have to necessarily be multiplayer. Anything self published counts as Indie. I'll list mine later when I can make a proper list.
I would have to say Mark of the Ninja, Risk of Rain, Castle Crashers, Starbound, Terraria, The Binding of Issac, FTL, Deadlight, Dust: an Elysian Tail, Legend of Grimlock, Cargo Commander, and Trine series.
To the Moon was an interesting game but I kinda found it boring, however the concept was good. The odd thing, I wouldn't mind seeing it as an Anime.
It told a story by means of interactive media. It is not a 'game' proper, and I approve. There are bonuses for it to be made in game format or as an anime. I think overall it was a net positive.
Rogue Legacy, Project Zomboid, Geometry Wars, Binding of Isaac, Rimworld. You guys should check out Underrail though. It's like playing Fallout 1 or 2.