Steins;Gate

A self-proclaimed "mad scientist" accidentally invents a time machine using a microwave and a phone — then watches as every attempt to change the past makes the present worse. Steins;Gate starts slow (the first 12 episodes are setup) but the payoff is one of the most emotionally devastating second halves in anime history. The time travel rules are internally consistent, the characters are deeply human, and episode 22 will wreck you. Based on a visual novel, it's rated 9.08 on MyAnimeList. Best experienced knowing as little as possible going in.