While a lot of indie games have decent gameplay and art technique, what really stands out to me is their fantastic art direction. Although there are tons of great examples, I only have space for a few. I want to talk about The Path, Samorost and Mondo Agency.
I was recently playing The Path and one of the things that really stood out about the art direction was the amazing character design. Characters for games should be easily recognizable as coming from their own game, and one of the reasons the characters in The Path look unique is their black and red color-scheme. It should also be clear what a character is about. The characters in The Path are nice because each character is built around a personality trait instead of their gameplay utility like in most games. Even though the characters in The Path share the same colors and are all girls, they're all clearly different from each other, which shows really superior design.
Great art direction doesn't have to be high tech, complex or detailed. I think Mondo Agency is one of the best examples of this. The abstract nature of the environments and characters means there are very few visual cues to tell you what to expect, inducing a sense of paranoia. The game world is also very dynamic, so the low-fi visuals are especially effective at communicating what's happening and how things work. Because the art is so consistently strange, I felt myself accepting the world the game presents. Some people may think this game is "too weird", but I think it's no more strange than films by David Lynch, and he has hundreds of thousands of fans.
This game is a good example of providing richly-detailed graphics without using a ton of high tech features. The photo-collage style graphics are really fresh, and give the game a cool whimsical vibe. I have no doubt that the style used in this game took a lot of experimentation before the right production techniques were found, but the result is very consistent and original. It goes to show how much impact picking the right style can have.
I think good art direction gives a game a consistent look that's both distinct and original. Can you think of any other indie games that have great art direction?