In simple negative phrases both are _correct_. Genitive sounds a bit more 'literary' but acc. is still correct.
A good list of exceptions you'll see following the Vasya's gramota link.
Cf. the French ne... pas _de_ ... .
One possible way to understand it (i'm not sure if it's correct) is 'partitive' function of genitive: 'some _of_ ХХХ' 'One _of_ us'
A haven't read*written/seen [a little] _of_ this.
Compare to Russian налить чай ('the' tea) vs. налить чая/чаю ('some' tea)
(Russian has a specialized form of 'partitive case' for masculine uncountable things, which differs from the genitive proper from: чая-чаю, сахара-сахару. Alas, in negations genitive proper sounds better... which effectively ruins my theory. But saying 'я не обратил вниманиЯ' I DO have in mind an image of 'attention' as a 'resource' of which I have paid nothing. So....
It correlates well with gramota's statement that in the situations with 'definite', 'the' objects (ЭТУ книгу) and with the proper nouns (Машу) acc. fits better)