Agh, there are so many! This is like the only type of gaming I do on my PC due to the fact that I'm poor and can't afford to upgrade XD
Easily one of my favourite series of indie games would be the Chzo Mythos games. They're a series of four point and click adventure games (much in the vein of the old LucasArts games like Monkey Island).
5 Days a Stranger
7 Days a Skeptic
Trilby's Notes
6 Days a Sacrifice
These are made by the great man that is Ben "Yahtzee" Croshaw (maker of the Escapist's Zero Punctuation).
I will assume that you have all played, or at least know how point and click adventure games go. If not, then I feel old and depressed. Anyways, the main thing I personally liked about them is that they are effing freaky as hell. Very psychological scares here (the type that Yahtzee always says he loves the most). Just note that if you do play them, be prepared for excessive blood and gore. While it's all graphics made in paint basically, it is still pretty freaky, especially combined with the story.
Basically, amazing games. Check out his site, FullyRamblomatic.com