Here are some of my favorite Indie comics, in their own special categories. *denotes for Mature Audience

RASL* (ending soon) by Jeff Smith
Glamourpuss* by Dave Sim
The Goon* by Eric Powell
Savage Dragon* by Erik Larsen
The Next Issue Project various artists
Prophet* (From issue 21 onward) various artists
Supreme* (From issue 41 onward) Erik Larsen and Cory Hamscher
Mouse Guard by David Petersen
Madman by Mike Allred (currently on hiatus)
The Walking Dead * by Robert Kirkman

Graphic Novels worth checking out:
A Contract With God* Trilogy by Will Eisner
Cerebus by Dave Sim (Various titles including High Society, Church & State, and Melmoth*)
Bone by Jeff Smith
Blankets* by Craig Thompson
Maus* by Art Spiegelman
Sin City* by Frank Miller
American Barbarian* by Tom Scioli
American Splendor* by Harvey Pekar (Various titles including “Cleveland” and “The Quitter”)
Any Empire by Nate Powell
China Town by Eric Powell

DIY comics
Cursed Pirate Girl by Jeremy Bastian
Lethargic Lad Greg Hyland
Spy Guy by Mike Kitchen
The Possum by Blair Kitchen
Axe Cop Ethan Nicolle
Blink by Max Ink
Elephant Eater Comics by Ryan Claytor
Afrodisiac* Jim Rugg

I know I’m leaving out a lot of GREAT people but this is the best list I can come up with at the moment.