Dungeon ni Deai wo Motomeru no wa Machigatteiru exceeded my expectations of it in a few parts, but it’s ultimately no more than an anime involving dumb wish fulfillment and tired cliches otherwise.
Shigatsu wa Kimi no Uso is a phenomenally animated and directed anime which attempts to affect its viewers emotionally. It succeeds at this somewhat, as it has a fair amount of issues.
Shin Sekai Yori stands on its own as an excellent installment in the domain of fantasy anime. There's a few scratches on the overall quality here and there, but this is mostly dismissible.
Mirai Nikki (Future Diary) is a 26-episode action anime series in which people battle for control of space and time using phones that tell the future, with as many plot holes as possible.