I'm not much of a Marvel kinda guy and I am very selective of what DC stuff I read, so I probably read more third party comics than anything else. Here's a list of some good non-big-two titles I have read.
Beneath the Dark Crystal - Current ongoing that is the sequel to The Power of the Dark Crystal, different writer, different art team but still holding up to the quality of the first series.
Elric - based on the Moorcock novels, originally published by First Comics they've been reprinted by Titan Comics in HCs, edgy dark fantasy with some great psychedelic artwork and use of color, recommended for teens and adults. There was also an original comic series put out by Boom called The Balance Lost that was good, and Titan Comics has put out a new series of GNs that are French in origin that are very dark and gothic.
Hellraiser - Boom published a Hellraiser series that acts as a sequel to some of the movies that Clive Barker himself wrote. Pinhead tries to buy his way into Heaven by trading places with Kristy Cotton. Highly recommended if you are a fan of the movies.
Hookjaw - Titan Comics reprinted this old 70's comic called Hookjaw, about an intelligent shark with a harpoon lodged in its jaw that it uses to spear and eat people, running off of the success of Jaws. Titan also rebooted it with a mini series that was okay, but I don't think it lived up entirely to the source material.
Lady Death - I'm a huge Lady Death fan. Brian Pulido is on the cutting edge of what the future of comics will be, crowdfunded GNs. Lady Death has a complex history spanning several different companies and continuities, but her comics now are better than ever before, her comics always deliver on blood and gore and TnA; recommended only for mature readers!
Lady Mechanika - Joe Benitez has been self-publishing his own book and it's been very successful. The art is great and the characters are fun. He has told some very unique and interesting stories set in a very detailed steampunk world. Recommended for teen readers.
Monstress - Dark fantasy with Lovecraftian monsters and some of the highest-tier art I've ever seen in comics. Very dark, edgy, violent, and lots of foul language, but with likable characters and rich, full world to explore.
The Power of the Dark Crystal - The sequel to the movie that was adapted into a comic book by Archaia, a division of Boom. Utterly fantastic art style and a very good story that ties in directly with the movie without conflicting with it at all. If you are a fan of the movie, trust me you will love this comic.
Robotech - The original Comico series is being reprinted by Titan Comics, it stays very close to the show and I'd recommend it for kids. Titan is also doing a reboot comic series that's been very hit-and-miss for me, it's changing lots of stuff, some of it good, some of it not so good, and the art at the beginning was terrible. However, they recently changed writer and got a great artist onboard, so I'm optimistic that it's about to get better.
Rust - A four part GN series put out in HC by Archaia. A really good series with a unique, cartoony art style about robots, I highly recommend it for kids. It'd make a superb animated film.
The Wormworld Saga - Ongoing GN series, so far there's only two parts; light-hearted fantasy, great cartoony digital art style, good for kid readers.