I HATH BEEN SUMMONED.
I'm just going to list my faves in several categories, in order of decreasing love.
Idols
1) Aikatsu!
This show is one that goes under the radar pretty often, partly because it isn't marketed much outside of Japan, and some of the art quality leaves much to be desired. But the series has an entire convention dedicated to it in Japan, which should suggest that it does at least something right; and it does. The characters are fun, the plot - while episodic in nature - is good enough to keep you watching, and the humor is rather well done as well. Granted, it's not brilliant comedy on the level of Amagi Brilliant Park, but it's enough to tickle most audiences. The CG is rather well done, and the music is pleasing as well. But what makes this show my fave in this category is how warm it makes you feel after each episode. It's about cute girls, doing their best to do cute things, and more often than not, failing. It paints a nice picture of the troubles and professionalism that come with being an idol, while still making you feel just happy. I would strongly recommend this show to anyone with a moderate interest in idols, it's just so much fun to watch. Granted, it lacks the drama that crowns several other shows, but it makes up for it with a host of characters that somehow never manages to bore me, even at 140+ episodes and ongoing.
2) Idolm@ster Cinderella Girls
Yes. Cinderella Girls. Not the 765 ones. I consider CG to be better than the original 765 because the character personalities are much more varied and just overall more interesting. Granted, there are some characters that grate on the nerves (namely Mio), but as a whole, I find the cast to be much more enjoyable, with personalities such as Ranko ("Oh, the tyranny of the Sun strikes upon us on this day!"), Anzu ("If you work, you lose") and Anya ("Спасибо"). The troubles they face are much more realistic as well, compared to those faced by 765. Let's face it, it's not likely for a professional sound crew to sabotage a performer's stage on request from an unaffiliated production company without there being major legal repercussions. Corporate reforms, on the other hand, are far more common.
3) Idolm@ster
That said, the original im@s is still a good show that you should not miss if you're into this category. With well-done drama and great camerawork, I would strongly recommend this show.
4) AKB0048 (+ Second Stage)
Now, this is where I might draw some hate, especially considering what I ranked under this. Many people refuse to watch this show on the sheer virtue of the fact that it has "AKB" and "48" in its title. While that's a sentiment that I understand, I'm sorry to say that they're missing out on a great show. I mean, where else can you watch idols with lightsaber microphones and homing missile lightsticks(Except maybe Macross?)? One thing to note in particular is that they did a great job using AKB's music. One major problem with many shows developed to promote music groups, is that there's a tendency to just toss in the songs whenever a soundtrack could ostensibly be required. Thankfully, AKB0048 avoided this problem. While watching the show, I never once felt that any of the insert songs was out of place. That's a mark of good directing and excellent sound production. While the plot is far from airtight, it does resolve itself nicely by the end of Second Stage, and the characters are all unique and differentiated enough to make this a show that manages somehow to sneak its way into my top 5 idol anime, despite personally not being an AKB fan.
5) Love Live!
Okay this is the bit where I probably draw flak. Let me start off by saying, I enjoy Love Live! I liked the show, I liked the humor, I loved the characters. A gander at my sig banner should inform you that I find Eri in particular extremely horosho. I love the concept, I love the characters, and while the CG certainly isn't much to write home about, it's not a pain to watch either. So why is this the lowest on my list? Because of the plot. Objectively speaking, the plot of LL is terrible. It's filled with cliches and bad plot devices. A lot of the "plot twists" are either predictable or so strongly telegraphed that the viewer is often left going "Yeah, saw that coming...". The other thing which LL does horribly wrong is melodrama. A bit of drama is good - it fosters character development and creates conflict and tension. LL, however, takes melodrama to an extreme, with characters often often experiencing dramatic wrenching of the heart over the smallest of matters. Anyone who watched the ending of S1 should know what event I'm referring to. Even in S2, the bit with the umbrella and the snow is so overdone, it crosses the boundary between "dramatised" and "unrealistic". That said, LL is still a pleasure to watch, but eventually I believe most people feel this way: We stay for the girls, not the plot.
Mahou Shoujo
1) Puella Magi Madoka Magica
Did anyone honestly expect something else to go here? PMMM is touted as a revolutionary anime that re-defined the genre, and for good reason. This show takes all assumptions anyone had about mahou shoujo anime and utterly destroys them, deconstructing the genre and reconstructing it as something so much more meaningful, a mission aided by a wonderful OST composed by Kajiura Yuki. Hype train aside, being overrated aside, this is the one show I consider a must-watch for anyone even remotely interested in Mahou Shoujo, and perhaps even a few who want nothing to do with the genre. This is one of the anime that serve as a valid argument for how anime can be treated as a work of literary art.
2) Mahou Shoujo Lyrical Nanoha ( + A's + StrikerS)
Because the power of friendship is unstoppable. Okay, jokes aside, Nanoha stands out among its brethren in several ways: first, the emphasis of magic as a form of technology, rather than something that just exists. Next, the consideration of magic as a military asset. Third, the notion of the big picture. In most mahou shoujo, the heroines are isolated warriors, fighting for their lives against large monsters in a pocket dimension where no others can see them. In Nanoha, these heroines are supported by an actual military force, along with with all the benefits (giant space battleships) and detriments (bureaucracy, regulation) that said support entails. With a likeable cast of characters and villians with believable motivations, Nanoha is a series which is sure to not disappoint.
3) CardCaptor Sakura
So, possibly the first thing you'll notice about this show is that it falls under the Tsubasa River Chronicle IP, meaning that you'll only gain maximum enjoyment from this show if you're familiar with said IP. However, on it's own, it still stands tall as a show with depth, a good plot, meaningful characters, and a strong focus on romance that manages to avoid being contrived or boring. As a good, well-balanced blend of light-hearted and serious, the show is a marvel of animation, and definitely deserves a watch. A classic.
4) Kill La Kill
Yes. I consider this show a Mahou Shoujo anime. It has transformations, flashy fight scenes and over-the-top weaponry. It qualifies. A show greeted with mixed reactions, some hate it, some love it. It has an interesting thematic focus on clothing and nudity, as well as notions of dependence and maturity. As a whole, this show seems ridiculous and over-the-top at first glance, but carries a wealth of depth, if you're willing to put in the effort to think about it. Some plot devices may seem contrived/cliched/predictable, but as a whole the show does an amazing job with regards to direction, execution and pacing. Watch the first few eps and then decide if you feel like it's too painful to carry on.
5) Binan Koukou Chikyuu Bouei-Bu LOVE! (Cute High Earth Defense Club LOVE!)
Well... it's not really anything special, but... just watch it. You'll see.
SPECIAL MENTION: Yuuki Yuuna wa Yuusha De Aru (YuYuYu)
I haven't actually watched this yet, plan to soon , but from what I've heard, it's good. Maybe worth adding to your list, if you have one.
Romance (Usually dramatic, not comedic)
WIP
Slice of Life
WIP
Fantasy
WIP
Shoujo
WIP
Other
WIP
This Season
1) Akagami no Shirayuki-hime
WIP
2) Gakkou Gurashi!
WIP
3) Idolm@ster Cinderella Girls
WIP
4) Charlotte
WIP
5) Overlord
WIP