One of the best is 'The Dark Knight Returns'. It presents an aged Batman coming out of retirement in a gritty, alternate future of the DC Multiverse. It's a story that challenges the traditional view of superheroes and their place in society.
The Aquaman movie had a mix of closeness and departures from the comics. It retained important aspects like the underwater world and Aquaman's powers, but added new subplots and character arcs. It's a matter of personal opinion how close one considers it to be.
The Batman Who Laughs is extremely popular. He combines the intelligence and skills of Batman with the insanity of the Joker. His twisted nature and his dark plans make him a fascinating character in fanfiction.
One interesting concept is the twisted versions of well - known heroes. For example, a Batman who has completely given in to darkness and uses extreme and unethical methods to 'protect' Gotham. Another is the alternate versions of the Justice League where their powers are corrupted and they become more of a threat than protectors.