Can anyone recommend any good LGBTQ comic books or graphic novels?  Super-hero or any other genre is fine.

Dykes to Watch Out For.   Alison Bechdel, since 1982.    http://www.paperbackswap.com/book/author/Alison+Bechdel

Fun Home, her childhood autobiography, won several awards.

Check out The Authority, which is a DC title that somewhat mirrors the old 'squad of superheros' style comics.  Features two gay superhero protagonists, Midnighter and Apollo. 

Some more major titles with gay subthemes include Ultimate X-Men (where Colossus is homosexual and expresses interest in/dates several other superheroes that I don't remember off the top of my head) and Hellblazer, notably in the Highwater arc.

Alpha Flight #106 is the issue where the character Northstar reveals that he is gay. It was the first comic approved by the Comics Code Authority that approved a comic to even mention homosexuality.

This is a manga series that has about 20 books in it and still going strong.

Banana Fish, Vol 1

Author: Akimi Yoshida

http://www.paperbackswap.com/book/details/9781569319727-Banana+Fish+Vol+1

Book Description:
New York City, 1985. A dying man leaves gay gang leader Ash Lynx a strange drug, the key to something called "Banana Fish." The mysterious potion will lead Ash to a disturbed Vietnam vet who remembers a massacre--and into brutal battle with the mafia over control of the drug.

Vice City: New York in the 80s... Nature made Ash Lynx beautiful; nurture made him a cold ruthless killer. A child runaway brought up as the adopted heir, hatchet man, and sex toy of "Papa" Dino Golzine, the East Coast's Corsican crime lord, Ash is now at the rebellious age of seventeen--forsaking the kingdom of power and riches held out by the devil who raised him, preferring a code he can live with among a small but loyal gang of street thugs. But his "Papa" can't simply let him go--not when the hideous secret that drove Ash's older brother mad in Vietnam has suddenly fallen into his insatiably ambitious hands.

It's exactly the wrong time for Eiji Okamura, a pure-hearted young photographer from Japan, to arrive in NYC and make Ash Lynx's acquaintance... and fall with him into the bloody whirlpool of pride, greed, lust and wrath unleashed by the enigma code-named Banana Fish...

Try:

Hothead Paisan: Homicidal Lesbian Terrorist -- Dianne DiMassa (lesbian)

How Lothesome (trans)

Awkward by Definition (bi author)

Ismoon

I was going to say Dykes To Watch Out For

LGBTQ is actually a huge field in manga, if you don't mind reading your comics backwards. I can reccomend a lot of series if you'd like. As for the person above that recc'd Banana Fish: I <3 you. That is an amazing series, I wish more people knew about it and read it.

Tales from the Closet about 10 years ago but don't know if its still out

The Strangers in Paradise series by Terry Moore was very long and complicated and revolved around the relationship between two women named Katchoo and Francine.  Early on you learn Katchoo is in love with Francine and as the series goes on, their lives get very complicated and their relationship changes in ways neither of them could have expected.  I was very happy with the way it all ended :)