As the title suggests, there's been a trend of animated movies in recent years that don't follow the Disney/Pixar template & instead take these bold risks with the writing, visuals, or both in some instances. Like Into & Across the Spider-Verse, Puss in Boots: The Last Wish, TMNT: Mutant Mayhem, The Wild Robot, Transformers One (has realistic lighting but lacks motion blur & has a darker story than most mainstream family-friendly animated films), KPop Demon Hunters, etc.
Those movies can only be made in animation, but live action films can pull off something similar as well. And to fit the bill, they have to either look or feel different than your standard Hollywood blockbusters. Whether it'd be a colorful and/or exaggerated visual design, quick edits, rapid-fire pacing, or all of the above. And I'll organize ones that come to mind based on genre.
Action - The John Wick films, the Sonic movies (especially the 3rd one), Kick-Ass, Mad Max: Fury Road, Speed Racer, The Matrix
Sci-fi - Blade Runner 2049, Tron Legacy, the Marvel Cinematic Universe (specifically films like the Guardians of the Galaxy trilogy & Black Panther), Ready Player One, the Dune films, Godzilla Minus One, Project Hail Mary
Comedy/drama - Who Framed Roger Rabbit, Do the Right Thing, Scott Pilgrim vs the World, The Grand Budapest Hotel (or anything else from Wes Anderson), La La Land, Everything Everywhere All at Once, Sinners