If it's crap ... We'll tell you
Mainly comics that don't require that much knowledge of continuity...
Blacksad is a great noir that is a most read, ultimate spider man vol 1 and 2, chew vol 1 and 2, wolverine old man logan, The Dark knight returns, Batman year one, the walking dead vol 1 and 2, Locke and key, Usagi Yojimbo vol 1 and 2, Hack/slash vol 1 and 2, V for vendetta,
Y: the last man all day; everyday. That is always my go to answer to this question. Also, Alan Moore's Saga of the Swamp Thing is thoroughly mind blowing once you get past the first issue.
These are my recommendations:
Watchmen is a fantastic book but that is something you would give to someone who has no interest in comics to get them interested, but i'm talking about something to give new readers that are already interested in it and just need something to get started.
Ok, then. Uh... Batman: Year One is really great.
Batman: Year One
Justice League: Year One
Green Arrow: Year One
Ultimate Spider-Man Vol.1
Thats all I've got for now, but if I think of anything else I'll be sure to post again. (Also, sorry for the obvious DC bias, when it comes to Marvel if its not Spider-Man I don't really care.)
Also, from what I understand Marvel is currently doing something similar to DC's Year One line called Season One for a number of their heroes. Probably worth checking out.
A CONTRACT WITH GOD
Any Year One books from DC. Watchmen, Superman Earth One and the newly released Batman Earth One, mainly because those don't require any knowledge of previous continuity.
Great comic with a very interesting origin story. The first volume could be taken as a story in itself, but goes on to give us muc more.
Obviously everyone knows Spider-Man. Ultimate Spider-Man gives us an updated, slightly edgier story than its main universe brother. Having less issues, it is far less intimidating to read than jumping into Amazing Spider-Man, and is also a great jump in for the Ultimate universe.
These are the two I suggest most, and were a big part of me getting back into comics in my adult life.