Space Dandy is a show I think everyone should watch. It's one of those shows that I can't promise you'll like, but I can promise you'll remember.
Then there's watamote. An anime about social anxiety. Depending on how much you can relate it can vary from being incredibly funny to tearjerking.
Now a couple more obscure shows which I love, but aren't that well known/well received:
Coppelion. Set about 20 years after a nuclear explosion made Tokyo uninhabitable, a team of 3 teenage girls who are immune to radiation due to being genetically altered must head into the city to search for survivors. I loved it because it had a lot of "what measure is a non-human" themes, but the general reception was not so warm.
Hitsugi no Chaika. So far my favourite anime of the year. I wouldn't know where to begin explaining the story, but it's essentially about a small group of travellers on a quest to gather certain objects. The plot is well-written and the pacing is spot-on, but what I love most are the characters. They all have their own motivations for what they do and there's no bad guy. There's a group of antagonists, but their reasoning for stopping the main characters is totally reasonable, and you could easily frame this story with them as the good guys.