Meh, I found Madoka to be overrated. It's like the Evangelion of the 2010s: popular because OMG SO DEEP AND SAD!!! etc. Madoka was better than Eva, though.
QB was my favourite character, but that should come as a surprise to no-one
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Parhelion69: I haven't actually seen it, but you might like Magi. It seems extremely popular at the moment and from what I know, it's action/adventure. I don't tend to watch that genre, sadly, so I can't help you much there.
But my general anime recommendations are:
-Angel Beats!. It's... shounen, I guess? I'm not sure what to classify it as. It's one of my favourite series, even if it is a bit sloppy. It's basically about a group of kids (well, teenagers) in purgatory. There's some comedy in it too, but it's mainly sad. I cried.
-Baka to Test to Shoukanjuu (aka Baka and Test). Comedy. It's fucking hilarious, that's all you need to know.
-Boku wa Tomodachi ga Sukunai (aka Haganai). Comedy. Most people probably find this bad, but oh my god the female characters are realistic as fuck.
-Chuunibyou demo Koi ga Shitai!. Er... comedy/drama? It's full of moe though, so if you don't like moe, AVOID AVOID AVOID. But if you're okay with moe, it's great.
-Clannad. Drama. Sad sad sad. You will cry. And you will laugh. But mainly you will cry.
-Danshi Koukousei no Nichijou (aka The Daily Lives of High School Boys). Comedy. The most hilarious anime in the history of anything ever. I have never laughed to much. EVERYONE NEEDS TO WATCH THIS MASTERPIECE OF EPICNESS.
-Gosick. Mystery. Might not be for everyone, but it doesn't have any fanservice or generic shit. Also, Victorique
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-Haiyore! Nyaruko-san. Comedy/romance. Cthulhu mythos turned into anime, basically. Kind of moe, but not so moe that you feel like throwing up.
-Kami nomi zo Shiru Sekai (aka The World God Only Knows). Shounen. This is something aimed at guys. And oh my god I love it so much. The anime adaptation isn't actually horrible, either! More people need to watch this.
-Kokoro Connect. Drama. I felt all the feels. ALL OF THEM. OH MY GOD. SO MANY EMOTIONS. If you want an anime with a good story, watch this.
-Sakigake!! Cromartie Koukou (aka Cromartie High School). ANOTHER COMEDY. I don't remember this one that well, except that it was hilarious. It has a Freddie Mercury clone and that alone should be enough of a selling point.
-Serial Experiments Lain. I'm going to classify this as "mindfuck", even though that's not a category. If you want something that's weird, out there, and doesn't make any fucking sense whatsoever, there's this.
-To Aru Majutsu no Index. Shounen. Some people don't like this, but I greatly enjoyed it. It's more sort of actiony than a lot of anime series out there.
This is going off of what I've seen. For specifically action things, I've heard Baccano! is good. Not sure about other stuff, though. Sorry!