Man is a most complex simple creature: see what he weaves, and how base his reasons for doing so.
Okay, to add some structure to this, why don't we all just suggest one series that epitomizes a very specific body of cliches that is probably still relevant today? Perhaps what comes to mind aren't "good" series, or even ones we like. The ones that give you the most bang for your buck.
I dunno about cliches, but I like Eureka Seven a lot and wouldn't mind recommending it (though Anonus may find some of the repetitive episode plots a bit tiresome)
it has its flaws but it's still really quite enjoyable
Each genre has its set of seminal shows and associated cliches.
For example, in the magical girl genre, two of the most prominent shows in the lineage are Cardcaptor Sakura and Sailor Moon. Cardcaptor Sakura (CCS) exemplifies the little girl being granted magical powers and thrust into a position of using them to accomplish tasks involving supernatural antagonists, and being aided by a cute animal-like mascot along the way. Sailor Moon (SM) also kinda does the same thing but has an emphasis on having a magical girl team, not unlike "sentai" (hero team) shows such as Power Rangers. CCS went on to be a more dominant influence on future magical girl shows, though both shows had their impacts. The Pretty Cure franchise is a major multi-series children's franchise that include elements of both CCS and SM. Meanwhile, an older audience interested in the magical girl genre was recognized by the creators of Magical Girl Lyrical Nanoha, which had a somewhat more mature viewpiont both in terms of characterization/storytelling features and fanservice, as well as subverting the "hesitant little girl gets amazing magical powers but is afraid to use them" trope by introducing some tropes common in shounen shows, especially mecha shows. Nanoha's lineage spawned a few successors that took this more mature angle, including Puella Magi Madoka Magica, which aimed to go full-dark with psychedelic imagery and total subversion of the typical magical girl story style -- it was certainly not the first to subvert the stereotypical positivity of the genre's storytelling, though it is probably the most famous example. MadoMagi itself has had its successors.
So, just right there, there's Cardcaptor Sakura, Sailor Moon, Pretty Cure, Lyrical Nanoha, and Madoka Magica, if you're interested in the magical girl genre specifically.
One could make a similar lineage map for other genres.
You're ignoring earlier iterations of the genre, and some key '60s-'80s cornerstones: Cutie Honey (hot lady fights monsters, aimed at young men), Full Moon wo Sagashite (the first to really take the sob potential to the next level), any of the zillions of Betwitched knockoffs, Key the Metal Idol (one of the first really dark subversions), Kiki's Delivery Service ('nough said)...
All this being said, Cardcaptor Sakura is a great place to start. It is very, very cute, and very, very gay. I'm serious. One of the main characters, Tomoyo, who is like Sakura's Batman benefactor and personal cheerleader, very explicitly has a huge doofy crush on her (and stuffs her into really weird outfits), and that's just the beginning of it. Also, it has the main character defeating weird supernatural forces through strategy, sometimes without actually fighting at all! It's really endearing.
If you want an entrée into some more esoteric, weird stuff, I'm always willing to help, although I have grown stronger in terms of mainstream works as well.
By the way, I'm not sure if you'd actually *like* Neon Genesis Evangelion, but I think you would appreciate how inventive it gets and how complex the characters and their relationships are. Martian Successor Nadesico and Tengen Toppa Gurren Lagann might be more your speed, but I haven't seen much of either—although I have seen Kill La Kill, which is by the same director as the latter (Imaishi! :D), and while I get the impression that it's the superior model, it is one of the few shows I thought I'd like less on rewatch and ended up loving even more.
As for Nadesico, the first Fullmetal Alchemist is really great, and for all his faults, Aikawa is a passionate man, so it's probably pretty good.
Comments
For example, in the magical girl genre, two of the most prominent shows in the lineage are Cardcaptor Sakura and Sailor Moon. Cardcaptor Sakura (CCS) exemplifies the little girl being granted magical powers and thrust into a position of using them to accomplish tasks involving supernatural antagonists, and being aided by a cute animal-like mascot along the way. Sailor Moon (SM) also kinda does the same thing but has an emphasis on having a magical girl team, not unlike "sentai" (hero team) shows such as Power Rangers. CCS went on to be a more dominant influence on future magical girl shows, though both shows had their impacts. The Pretty Cure franchise is a major multi-series children's franchise that include elements of both CCS and SM. Meanwhile, an older audience interested in the magical girl genre was recognized by the creators of Magical Girl Lyrical Nanoha, which had a somewhat more mature viewpiont both in terms of characterization/storytelling features and fanservice, as well as subverting the "hesitant little girl gets amazing magical powers but is afraid to use them" trope by introducing some tropes common in shounen shows, especially mecha shows. Nanoha's lineage spawned a few successors that took this more mature angle, including Puella Magi Madoka Magica, which aimed to go full-dark with psychedelic imagery and total subversion of the typical magical girl story style -- it was certainly not the first to subvert the stereotypical positivity of the genre's storytelling, though it is probably the most famous example. MadoMagi itself has had its successors.
So, just right there, there's Cardcaptor Sakura, Sailor Moon, Pretty Cure, Lyrical Nanoha, and Madoka Magica, if you're interested in the magical girl genre specifically.
One could make a similar lineage map for other genres.
course i was watching a severely mangled English dub
magical girl team: Sailor Moon
traditional magical girl + mecha influences: Nanoha
magical girl elements + fantasy adventure: Magic Knight Rayearth
magical girl elements + romantic drama + other stuff: Mai-HiME
magical girl + character study: Uta~Kata, Umi Monogatari
magical girl + darker: Uta~Kata, Madoka Magica
something about being post-MadoMagi: Yuuki Yuuna
it's, like, the gentlest children's movie i've ever seen, it's really sweet
miyazaki movies are great anywya