The Meaning of Life, the Universe, and Everything.
I'm going to jump right in here and say that I'm probably getting way too in depth with this but oh well.
My first recommendations would have to be Cowboy Bebop, Trigun or Neon Genesis Evangelion. Three classic animes which all have much controversy surrounding them and their reviews.
Next, we move onto the animes that relate in some way to Akame ga Kill. Death Note, Zettai Karen Children: The Unlimited - Hyobu Kyosuke, Kyoukai no Kanata, Strike the Blood and Mahou Sensou, Mahouka Koukou no Rettousei all have some similar themes that can relate the Akame ga Kill, mostly the fact that they all contain strong protagonists whom face tough challenges.
Hamatora, K Project, Black Bullet, Aldnoah.Zero, Durarara!!, Zankyou no Terror and Ryuugajou Nanana no Maizoukin are also good. Whilst the reviews on many of these animes are rather negative, I got a fair amount of enjoyment from them. These all do slightly relate to Akame ga Kill, but not so much as the ones mentioned above.
You should probably tell us what you have and haven't seen. Also, it would help to know your interests.
Try Death Note, Ore Monogatari, Sword Art Online, Log Horizon, or Soul Eater. All of those are well animated and somewhat short anime with lovely characters.
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My current avatar is Gyro Zeppeli from the popular manga Jojo's Bizarre Adventure. He's my favorite character. I love his optimism, dry humor, and his ability to do considerable damage even without a stand.
I beg to differ. In my days of being an anime fan I've encountered some extremely negative and controversial reviews/opinions on both of them.
If you want to beg to differ, you'll need to do better than vague personal anecdotes. I'm sure someone, somewhere out there, has written scathing diatribes against Cowboy Bebop. That doesn't change the fact that it's notorious for being an unusually well respected and uncontroversial series. Same goes for Trigun, though to a lesser degree since it does meet with some mixed opinions, but not much in the way of controversy. Saying that Cowboy Bebop is controversial remains a pretty quick way to discredit yourself.
If your looking for a new anime from this season, critics say (and I) that Charlotte is by farrr the best art/animation tying God Eater. Also the characters and plot is solid and it does not have alot of fan-service if you know what I mean.
Sword Art Online is also very good. However never read comments on YT about it as people always spoil end of season 2. *sob*