... is for people who have no souls. ( ͡° ͜ʖ ͡°)
If you can't make it through episode 7 or 8 (the end of the first arc), then you should drop it then and there. Like I said before, it's formulaic, but if you don't like the formula, don't bother. The show's claim to fame doesn't happen until well into the second season.
The apologizing is based on Japanese culture. Normally it's played for laughs, but Western culture considers it offensive/passive-aggressive. If you don't like timid characters, you won't like the next arc, you won't like the end of the first season, and you won't like the beginning of the second season.
Based on these, I might suggest Fate/Zero. It's a battle royale with Pokemon based on mythological figures. Excellent fight scenes, and your standard Urobutcher utilitarianism fare. First episode is an info dump, but watch it anyway. It helps to establish a lot of rules in the show's world, and that will carry over if you ever wanted to watch Fate Stay Night. Subs and dubs both available, 25 episodes.
If you want a show that's more like SnK/Attack on Titan, I might suggest Gate: Jieitai Kanochi nite, Kaku Tatakaeri. It follows a similar idea as SnK/AoT, survival against an attacking whatever; however, it doesn't take itself nearly as seriously. Story is unfinished, but there is a season 2 coming out soon. Subs only, recent airing, 12 episodes.
Mentioning Btoom! does actually make the No Game No Life rec make sense.
>> nisekoi
>> plot
>> mfw
Not sure if you've seen Nisekoi's second season, though.
Bakemonogatari fits pretty well here. Don't be thrown off by the unique art style or reading the random flashcards. They're just quotes from the novels describing the scene. They add nothing. Beware of Japanese puns. The show is not in chronological order, but the intended watching order is the airing order. People are free to disagree, but they're also free to be wrong.
If you want to watch something that reverses the genders, you could watch Ouran High School Host Club.
I can't say anything about Gangsta, as I've only heard reviews calling it an intense disappointment and I don't intend to investigate myself. I haven't seen Planetes, but I know it's about space janitors.
I vehemently recommend against starting this show. Unless you have an understanding of 2005-2010 Japanese politics or post-reconstruction Japanese history, a strong understanding or tolerance of Japanese culture, or a library of knowledge concerning 2000-2010 anime, large chunks of this show's comedy is completely lost after the first six episodes.
It's being split into three movies. The first is coming out on January 8th, expect speedsubs 12 hours after the first airing.