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.
Hunter x Hunter is an anime defined by how strongly it sets up its engagements and general character portrayals. Most of its other merits are contained solely within one of its seven arcs.
Ginga Eiyuu Densetsu is an above average series that about anyone can enjoy. However, it isn't the "greatest anime ever," as anyone within its dedicated fanbase might have you believe.
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.