A lot of times these anime girls with big boobs that get shoved in you're face are just a big bundle of cliche'. NEWS FLASH. Cliche's should ENHANCE the character not BE the character!
Normally, anime/manga that have big boobs, or characters with big boobs that aren't constantly shoved in your face ever get very popular just a few examples.
Bleach (Big boobed girls, that have had jokes, but aren't CONSTANTLY thrown in you're face...even though KT's had fanservice spreads...especially the new 'want to drown us?' XD, ironically the lead female is small breasted and is the most popular bleach female by a big leap)
One Piece - Also big boobed girls that don't get shoved in you're face
Fairy Tale - Actually, this has A LOT of jokes about them, however they get lower as it goes on. And they aren't annoying.
Naruto - Very few big boobed girls, and the 2 more popular girls (Sakura and Hinata) are normal breasted
Gintama - Has there ever been a big-breasted girl?
Code Geass - Even though Milly pointed out Shirley having big boobs...they aren't that large actually. Also Kallen has had A LOT of fanservice, however her breasts aren't overly-big and she doesn't get THAT much fanservice.
Claymore - Once again, how many big breasted girls are there?
Death Note - Also none to very little big breasted girls (I haven't read it in a while so I don't remember)
Inuyasha (Haven't read this in I don't know how long, but I believe it wasn't that fanservicey, and the main girls didn't have big breasts)
Ouran High School Host Club - No big breasted girls. Haruhi is very normal. Or 'petite'.
Vampire Knight - I THINK there is a bit of some big breasted girls here, but not huge. And Yuuki is rather normal as well.
Perfect Girl Evolution - No explanation needed.
Many Others as well (I read a lot of manga, most of them have normal boobs, or big ones that aren't shoved in your face)
Also, many other mangas that aren't popular that I read I believe would be soon-to-be
I believe the reason to be is that these anime's/manga's tend to be more 'realistic' and many times people tend to think that these big boobs make everything much more juvenile and seem to be only shows and manga's that want to feed hormonal boys/men's fantasies. So many times this is true, that the anime doesn't even HAVE to be quality to get viewers just because these males want to endorse themselves in big boobies. (This doesn't go for every male...just a lot)
Many girls (and boys, but to a lesser extent) just don't take these anime's and manga's seriously, because I mean.
For us girls who play sports. I SWEAR every time I see a big breasted girl not well covered up juggling her breasts while fighting makes me go 'OUCH!'. And it just makes the whole thing less realistic for me.
Big boobs don't necessarily degrade the anime or manga, however if they are thrown in your face, completely disproportional, and just WEIRD looking, it just makes the thing go, as someone here said 'was that really necessary?' There are anime that have this, that don't make the whole story suck, but the majority of more popular ones are as I listed above.