Ah, I remember watching Anohana. Sadly, I don't remember much beyond a few key points, beastly forgetful as I am, but I do recall that it was indeed the crushing type of story.

If you liked Gurren Lagann, perhaps you might want to try Gunbuster and Diebuster? In some ways, TTGL is Diebuster's spiritual successor, and Diebuster itself is Gunbuster's indirect sequel and sort of spiritual successor; Gunbuster is something of a grandfather to modern super robot shows, and Diebuster has both that and groovin' magic and stardust tears (you'll get it). And if you're in the mood for something similar yet different (and without the robots), Kill la Kill is often considered something of a spiritual successor to TTGL in its own right, with high-octane, goofy slapstick and lots of action, though it is rather... striptacular, with people wearing often a lot less than they probably should, for a reason that actually makes sense in the context. Speaking of which, quick word of advice in case this is important to you, but both -buster shows have no qualms about showing boobs, either, though it's done in a natural and mostly tasteful way.

And to try and hit most of your genres at once (all at once is a little hard) as well as I can, consider maybe Mahouka Koukou no Rettousei (The Irregular at Magic High School), which has something of a genius overachieving supersoldier and his equally overachieving sister kick ass and chew bubblegum in a magitech-filled setting a few decades into the future, or perhaps the Toaru (or Raildex) setting, with Toaru Majutsu no Index (A Certain Magical Index), Toaru Kagaku no Railgun (A Certain Scientific Railgun), and Toaru Kagaku no Accelerator (A Certain Scientific Accelerator), each story following a separate middle- or high-school protagonist in a world where magic and superpowers developed by science coexist but are rather at war with each other, with some sort of grand scheming behind it all. Season 3 of Index was way too fast and completely impossible to follow without reading its source novels, I'm afraid.

Incidentally, if you haven't watched it, both Hagane no Renkinjutsushi (Fullmetal Alchemist) shows are very good, to say nothing of the fact it's one of the quintessential shounen fantasy adventure series; they depict the story of two brothers who used alchemy to touch upon what they were not supposed to and were harshly punished by it, and then start to look into a way of fixing what they ruined. The older anime deviates from the (back then still ongoing) source manga after catching up, whereas the newer one has a weaker buildup at the beginning but then tells the rest of the story correctly, so I'd watch both in the order they were made.

For something deeper and that will still keep you on the edge of your seat, look no further than Shinsekai yori (From the New World); I will say about it only that it takes place in what seems to be an utopic world but that could not be less utopic, so give it a few episodes so that you can actually find out what you're in for. It has some jarring shifts in art style in certain episodes, and many have expressed their dislike of the content of certain scenes, so be warned you might be in for a shock that does not relate to the plot every now and then. Word of warning: it is something of a psychological thriller/horror; it has no jumpscares, but the content can be the stuff of nightmares. On a related note, there's also one of the kings of psychological stories, Monster, and its trip into the mind of a sociopath. It's often slow, and 74 episodes is nothing to scoff at, but it pays. Again, the content can induce nightmares.

Meanwhile, for a less deep, less philosophical, less serious, less of an edge-of-your-seat deal that is still quite something of a brain wrecker in its own right, I'd recommend Jintai (Jinrui wa Suitai Shimashita / Humanity Has Declined). It's a bizarre, comedic, and light-hearted take on... the notion of the end of the world, of all things. And for the philosophical outlook of a traveller with a talking motorcycle who visits places and just takes the concepts in, never interfering in what she sees, Kino no Tabi (Kino's Journey) is something of a winner. I haven't yet watched the new one, but it's said that the old one is better. And if you like that, perhaps Majo no Tabitabi (Wandering Witch: The Journey of Elaina) might do the trick, too, though it's a bit lesser as a story (even if it looks better on an artistic level).

Now, what follows here is something of a shotgun approach with anime I consider very good at their own genres but often overlooked; they're perhaps not the best or most famous, but they're definitely worth a watch. First off, if you've watched and liked either Baccano! or Durarara!!, consider watching the other one with a very high priority; they're both from the same author and very similar in several ways. And if you haven't, well, give them a shot, too; they're odd and hard to explain, with Baccano! involving immortals and gangsters and insane people and taking place in the US in the 1920s or 1930s or so, and Durarara!! involving gang wars, a headless rider, flying vending machines (yes, you read that right) and even more insane people, only taking place in modern-day Tokyo. Crazy? Hell, yes. Fun? Hell, yes. And while we're touching upon gangs, Black Lagoon tells the story of a run-of-the-mill Japanese office worker who one day found himself first unwillingly mixed up with a smuggler-pirate-mercenary outfit operating from a mafia-ran city in Southeast Asia and subsequently forced to embrace that as his new life... and then became quite good at it.

For more robots, aside from the -buster shows, perhaps Fullmetal Panic! will do the trick? Some form of (kind of magical?) lost technology that only some people can somehow access exists in its world, people are warring over that stuff, and an antisocial mecha pilot from a mercenary outfit is assigned to guard one of those people. At school. And the target he's guarding is a tsundere. The second season, Fullmetal Panic? Fumoffu, is actually not a second season so much as a sort of self-parody, and it's very good, too; the story proper continues with the third season (confusingly called Fullmetal Panic! The Second Raid). The whole thing is pretty funny.

On that note, we shift to a more comedic department. I think Hataraku Maou-sama! (The Devil Is a Part-Timer!) is a good hit; it tells the story of a demon lord who got sent all the way to Earth and has to work regular jobs to survive. It has some quite amusing romantic turns, too. By the way, ever wanted to know more about how anime is made? If so, consider watching Shirobako. It's a positively wonderful comedic slice of life about making anime. And if you like it, perhaps try New Game!, which is almost akin to a lesser Shirobako for game-making, but with a greater focus on slice of life and very little in the way of actual game making. And since most of it is pretty slice of life-y, how about cute girls doing tank drift? Yes, I said tank drift. If that's your thing, Girls und Panzer is your stuff, and "panzer vor" is your catchphrase.

And if cute girls doing cute (and sometimes weird) things (with cute but weird catchphrases) strikes you as a good idea, you may also be interested in the school mystery club of Hyouka with its ever so memetic "ki ni narimasu" catchphrase. But if you want a school mystery without the cute girls doing cute things side to it, there's always Tasogare Otome x Amnesia, in which a student and a ghost try to solve the mystery of the latter's death. It sounds like it's horror, and I seem to recall it has a little, but if I'm not mistaken (and I could be) not so much. The OP has some beautiful imagery, too.

And since we're also going for some weirder shows, perhaps Suzumiya Haruhi? The first season is confusing and has a bunch of different episode orders depending on what suits your fancy, and the second season didn't help by dedicating eight episodes to the Endless Eight arc (watch only the first and last of them, or at most one more from the other six, and ignore the rest; trust me, you won't miss a thing), but the story underneath it is pretty solid despite all the trolling on the part of the staff.

Okay, I'm running out of ideas again. :D What I still have off the top of my head is straight up horror, stuff that panders to the male audience perhaps a little too heavily for a general recommendation, or other stuff that is hard to recommend blindly. I also noticed that you didn't mention sci-fi, so I tried to steer clear from what leans more heavily that way; of course, mecha is sci-fi to begin with, and Raildex has a fair bit too, so it was always a non-starter to try and ignore it completely, but I still tried to not go there too much; if a phone microwave (temp name) that travels in time is interesting to you, I have a few ideas in that department. And yes, the phone microwave (temp name) is a reference to one of my potential suggestions; have you watched it yet? :)

And you're welcome! You know, I think I took over two hours to write this message (and if I count all messages, it's probably about four hours in total), but it turns out I'm actually liking this trip down memory lane a great deal. :D