Wow...what a big question! I'm going to skip reading everybody else's answers (but the ones I looked at were full of useful info).
A manga tells a story. It tells it with both pictures and text. So what makes a great manga?
1) a good story. There's no way around this one. What makes a story good (interesting to readers)?
a) Characters who seem real to the reader (people are interested in people). examples: KareKano, Appleseed, Yokohama Kaidashi Kikou, Karin
b) in an interesting situation (show me something I can't see at home) examples: Mahoraba, Planetes, Midori no Hibi, Gunslinger Girl, Fruits Basket
c) doing interesting things (because interesting people doing interesting things is interesting) examples: Ghost in the Shell, Yakitate!! Japan, Alice 19th, Crying Freeman
d) changing as a result (this follows from a) - real people change in response to experience) examples: Chobits, Ai-Ren, Ghost in the Shell
e) goes on just long enough to tell the story, then ends neatly. Examples: Midori no Hibi, Mahoraba, Ai-Ren, Ghost in the Shell, Alice 19th.
2) good art. Great art is not required, but is a bonus. But the art has to be good enough to help tell the story. What's good?
a) good page design. If I have to hunt to figure out which panel comes next I'm not going to be as involved in the story. Chobits and Midori no Hibi are good examples.
b) character designs that convey emotion well. In a novel you do this with text, in manga you do it with portraiture. Examples: KareKano, Midori no Hibi, and Karin.
c) distinguishable characters. Do something so I don't confuse the male lead and somebody's uncle. don't be like: Love Hina, Fruits Basket
d) consistent backgrounds - you have to give a feeling of place, and if the place is the same it should look the same every time. Chobits and Mahoraba for the win here.
e) good frame composition. Avoid clutter. Whitespace is the greater part of art. Don't be like: Love Hina, Fruits Basket (sometimes).
3) good text. Yes, even though it's pictures, the words tell a lot of the story. Reading manga in translation is hazardous because the scanslators may butcher good text. I scanslate Futari Ecchi and believe me - translations move meanings all over the map. What's good?
a) words that fit the character. If the character wouldn't say it that way, don't write it that way. Would he even say it at all? Should it just be a picture? Some of the most powerful moments in manga have little or no text. Examples: Midori no Hibi, Kare Kano, Planetes, Yokohama Kaidashi Kikou
b) Words that get to the point. Unless the character is supposed to be chatty, less is more. Appleseed and Ghost in the Shell are both bad examples.
c) extra points for a good turn of phrase, but remember - you're not writing a novel here.
Note that I'm not pointing out perfect examples of anything. There are better drawn mangas than the ones I mentioned, and there are better written ones as well. I think the big deal is that if the story and characters are good enough, the drawing and text need to not get in the way. That's all. So the art in Mahoraba, Midori no Hibi, and Ai-Ren for example, is good enough that it enables a good story to come through. Chobits actually tries a little too hard at art sometimes and hurts the story (I think, anyway).
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