I have read quite a few indie comics. My tastes run more towards action orientated books, but I am in no way adverse to other stories. You will also probably notice that most of the books I list below still have elements of action or suspense.
Like Yogi said, “I yam what I yam.” Anyways, my recommended readings:
“Girls”, by the Luna Brothers, is pretty great.
Anything that Moebius touched is gold. Especially his stuff with Jodorowsky or his Blueberry work. Check this AirtightGarage.Tumblr.com page for more Moebius.
I have not read enough of it to give a definitive answer review, but I have enjoyed every bit of “Love and Rockets” that I have read.
I cannot fail to mention “Maus”, but that is kinda like high school homework reading at this point. It is really good though. I mean, it is a Holocaust Survivor’s account, so it is not the happiest book in the world, but it is excellent.
“From Hell”, by Alan Moore and Eddie Campbell is the best book that Alan Moore ever did. Seriously. Warren Ellis thinks so too. Alan Moore has a recurring theme in his books, wherein Superhero characters are typically shown to be either nostalgic homages to a time gone by (Tom Strong, ABC Comics, etc.), or the tights brigade are shown to be kind of silly or wrong for what they are doing (basically everything Alan Moore wrote for DC boils down to “Superheroes are dumb”). But, “From Hell” is a brilliantly researched and intricately told crime investigation story, while also being a glimpse into the history of London. It is really, really good. The movie was not terrible… but read the book.
I am also a big fan of Sunday Newspaper comics, and I have the slipcase boxed set of “the Complete Far Side”, by Gary Larson to prove it.
I want to own all of “Calvin and Hobbes”, by Bill Watterson… but that is a purchase to be made after I figure out where to store all the stuff I already own.