The question of what does and does not make a good adaptation is one of the most complicated in the art world. Some say it's adapting the source material as close as humanely possible, down to the last detail, others say that it's getting the themes and ideas underlying the story right while changing the source material as you need to in order for it to better fit the medium it's being adapted into.
Both ways can either yield revolutionary results, or render you an utter laughing stock, so there isn't one surefire way to succeed. Especially when adapting manga into anime.
Anime is DOMINATED by adaptations of famous manga, from true blue classics to flash in the pan fluff. They have established fanbases, the story is already thought out for you, and the artstyle is generally easy to adapt into animation. But sometimes the anime team either has to alter the material due to various limitations, or they just have a different idea for where the story is going.
While several anime on this list are genuine classic anime in their own right, as adaptations, they utterly fail at bringing their source material to the screen.