These are comics you should read. Either they are excellent or they are must-reads for their character. I am probably biased towards Superheros, and DC at that(and being even more specific: modern DC.) I am not even going to list a lot, because I think it would bog down someone else trying to give out suggestions. So please do.
You might not want to buy them. Understandable. When I download, I use Demonoid.com (requires membership) and 4chan/co/'s /rs/ - Rapidshares (not safe for work). I am sure public torrent sites work too, along with other type of sources. (Like Yahoo Groups? Whatever.)
You might need a "cbr" reader to open these files. Link to download at bottom of post.
Green Lantern
Everything from "Green Lantern: Rebirth" and on. Geoff Johns has taken on the Green Lantern Corps(and his nostalgic love, Hal Jordan) as his own personal project and the dual series(Green Lantern and Green Lantern Corps) has benefit from it greatly. This is personally my favorite on-going. To list it...
I've found a good torrent for this:
Demonoid.com - Complete Green Lantern/Sinestro Corps War
Great thing about this one it clearly presents a order to read it. It goes up to the Sinestro Corps. From there you would continue reading the two series which at the moment are apart of the whole "Rage of the Red Lanterns" arc and is heading towards the climatic "Blackest Night" DCU event. (PS: Skip the fucking terrible 3-part "CORPSE" story if you get to it, hardly canon)
There is a Green Lantern movie coming out Dec 2010. It features cameos from Guy Gardner(currently in my avatar), some other in-jokes, and even Alan Scott.
Justice Society of America
The original JSA predates teams like the Justice League, Legion of Super-Heroes or even Marvel's Avengers. It was the first superhero team in the history of comics. Even in the DCU they are treated as such. A new series by Geoff Johns could be summed up by saying "The old heroes of yesterday train new heroes of tomorrow." This means you won't see characters like Superman or Batman, but you will see the original Green Lantern and the original Flash training unknowns like Stargirl and Damage. The cast is huge and constantly changing/growing. The series goes really deep within the DC universe, so it could be confusing for people new to it, but at the same time a great introduction. Johns has written two volumes, second ongoing. The second ties-in to Kingdom Come.
"JSA" (1st)
Demonoid.com - JSA (1999-2006 series)
"Justice Society of America" (2nd)
Demonoid.com - Justice Society of America (2007 series, to February 2009)
(I suggest skipping JSA Strage Adventurers and all of JSA Classified save the Power Girl arc if you like Power Girl. Maybe go back and read them, but they are not written by Johns for the most part and it suffers. If you want to make the download quicker, don't even download them)
Kingdom Come
This takes place on an alternate DCU(Earth-22). It is in the future where Superman has retired and disappeared. Batman is old. "New Age" heroes are reckless and care little for civilians. The Spectre(an agent of vengeance who works under God) has asked a priest to help him judge who is at fault for a coming tragedy. The series is Alex Ross's masterpiece and has influenced the DCU long after it. The second volume of JSA ties into it. I could see this not being a good read for people who are new to DCU. It had a loosely-tied in sequel series named "The Kingdom." I found it to be pretty meh and ignored it.
Demonoid.com - Kingdom Come and The Kingdom
Superman
Morrison's All-Star Superman. Read this goddamn it. Read it. It is the best Superman story ever. Maybe my favorite comic series, ever. 12-part.
Demonoid.com - Complete All-Star Superman
The Walking Dead
(Image's) On-going Zombie Apocalypse series. The depressing and hopeless kind. Incredibly compelling and addictive. If you want a good zombie story, you want to read this. In my opinion it beats anything we've seen concerning the subgenre. Again, a torrent:
Demonoid.com - The Walking Dead Issues 1-57
Watchmen
I don't know if I need to introduce Alan Moore's Watchmen. A movie is being made. The book is certainly going to be better. I am unsure if it is better to watch the movie first or read the book first. You might either gain certain appreciation for the movie's little touches or you might find the movie underwhelming. A tip for those who read it for the first time: Don't ignore the "boring" pirate comic or in-universe media at the end of each issue. Or if you do, read it when you reread it. You'll find just how detailed the story is.
Demonoid.com - WATCHMEN #1-12 (1986) (Remixed) (High Res) (Minutemen-DTs&TheKid)
There are also narrated and animated "motion-comics." From what I've seen of them they are pretty entertaining and the narrator is really good.
Demonoid.com - Watchmen - Motion Comic 1-12
A cbr file is the preferred method of reading comics online. You can get a reader here:
CDisplay Comic Reader
Feel free to post your own suggestions. I am not quite finished(I haven't even gotten to Marvel yet), but this is enough for now. As many of these series are on-going these torrents won't contain the entire series and if they do, they will quickly be outdated.
Some Pictures to go along with the series I mentioned above.
Motherfucking huge Justice Society of America picture.
Spoiler: show
The Rest
Spoiler: show