Here’s some anime I’ve recommended to people recently in no particular order:
Princess Principal – a spy thriller set in steampunk not-London. All the fun parts of a James Bond movie, but a full series and a couple of movies.
Sakura Quest – a recent college graduate reluctantly becomes the “queen of the Chupacabra Kingdom”, aka tourism promoter for an obscure rural town.
Yamada-kun and the Seven Witches – a semi-deliquent gets deeply involved with the small group of classmates that secretly have minor superpowers. This is after suddenly switching bodies with the head of the class.
Katanagatari – a tactician on a quest to recover ten “blades” (really a variety of fighting related equipment) recruits an island recluse to help her recover the weapons. Each 45 minute episode focuses on defeating a new unbeatable warrior to claim their weapon for the shogunate. The dialog is incredible. (Also, its unrelated to the Monogatari series, as in Bakemonogatari, Nisemonogatari, etc.)
Scum’s Wish – it’s basically all about unrequited love, sexual frustration and what people to to coup with it. The characters are all deeply flawed, but in believable and ultimately sympathetic ways. It really explores the messier aspects of romance that most anime shy away from (also, people actually have sex), without being a smutty soap opera like Love and Lies and Domestic Girlfriend (not that those aren’t entertaining in their own right)
Haibane Renmei – a story taking place in a secluded town where there are normal people, and Haibane, which are angel-like being who hatch from egg/cocoons. Every Haibane is of varying age, and has no memories of their past life beyond vague dreams. They are not allowed to have money, they report to a secretive priesthood and absolutely cannot leave the walls of the town. It’s fairly underwatched, but generally the people who have seen it love it (and I agree). Its a bit slow, but the world building and ending are very solid.
Honey and Clover – a drama following a group of nearly graduated art students start to transition out of school and establish their own identities. I really liked how it dealt with the characters developing as people. The romance is generally pretty good (not a lot of happy couples, though). Plus I appreciate that it’s mostly about adults with jobs, which is weirdly rare for anime.
My Bride Is a Mermaid – this is a stupid comedy, but it does it really well and consistently throughout its one season. Maybe I have bad taste, but I remember it being hilarious.
Sleepy Princess – another stupid comedy. This one I watched more recently, and after the first episode I thought “that was funny, but there’s no way they can stretch this joke any farther and it still be funny”. And I was wrong. It stayed funny the whole time. It’s about a kidnapped princess terrorizing her demon captors as she tries to make her room more comfortable (killing many in the process).