Was some discussion about isekai genre. I have seen some of it.
Magic Knight: Rayearth
Seen anime on TV and on anime club. 3 high school girls from different schools are summoned to fantasy world to fight against some evil dude and his minions. This is clearly aimed for the children and therefore wasn't really enjoyable for me.
The familiar of Zero
I've got all anime seasons on DVDs. Female lead is magic school student from bottom of the barrel. Her attempt to summon a familiar gets her a NEET from Japan. Heavy on comedy, romance with some kissing, and abuse against male lead, series has some good characters and character development. Also bunch of stuff that don't make much of sense: one student blows a whistle, bunch of knights crash through the doors and windows, some kind of trial is being held against one of the students, and teachers & rest of the school staff are nowhere to be seen nor has their absence ever been explained. What the Hell?
Konosuba
Translated light novels and manga are available at least for Kindle and Apple's iBook software, anime is at least on Crunchyroll. Japanese NEET dies of heart attack and goddess of water ask him to go to fantasy world to fight demon king, along with 1 thing of NEET's choice. He choose goddess herself. Unfortunately, goddess don't have much in the way of knowledge, skills, nor fighting ability aside holy attacks against undead. 2 other misfits join them: wizard, who can cast 1 powerful explosion in day and nothing more, and crusader, who can endure punishment better than her plate armour, but can't hit broadside of the barn. "My party can't be this dysfunctional". Despite being surrounded by beautiful girls, male lead don't seem to have romantical interest for anyone, though light novel #5 brings some development on that front. Anime is decent adaptation which puts more emphasis on scenes that light novels skim over but also make some cuts, and manga only makes cuts without adding anything new.
Re:ZERO -Starting Life in Another World-
I have watched anime on Crunchyroll. Japanese guy (again) suddenly finds himself inside of unfamiliar city in fantasy world. He thinks he knows something about isekai genre, but I have a feeling he don't know about The familiar of Zero and Konosuba. And soon enough things go worse for him than either for Saito or for Kazuma: he dies. Surprise: he ends up going back in time being alive, and looking for ways to survive through incoming disaster after disaster. Heavy on angst and PTSD, but this time there are good justifications for that: dying horribly and repeatedly has to suck big time. And he sucks it up and moves on. Along the way he meets girls and there is some romance going on.
GATE: Where the JSDF Fought
That is the official translation of the manga, and I've got it. First volume at least, and I'm wondering why more hasn't come by now. Stargate (of sort) appears in middle of Tokyo and fantasy army comes through of it. JSDF curb-stomps it and goes through the gate. Main character is lieutenant otaku commanding a recon squad. As he and his squad do reconnaissance, they come across with elfs, dwarfs (looks like anyway), dragons, cat girls, bunny girls, mages, immortal demigoddess loli... Yeah. But there is a war going on, and war is Hell. And bloody, even without colours. And rape. And bathing. Manga has a good number of pages that goes against the forum rules. Anime is available on Cruncyroll and HIDIVE, and it cut & censor whole lot. Lieutenant gets close with some of the fantasy girls, but he don't have romantic interest for anyone and stonewalls any advances the girls make towards him.
[New Life+] Young Again in Another World
Light novels, translations available at least for Kindle. Why did I even bought this? Oh, right, this:
"He was, therefore, understandably upset when he woke up again in an empty space, devoid of memories, with a young girl in a tunic rambling on and on about how she’s God. So, he did what any reasonable person would have done under those circumstances: he sent the girl flying with a kick to the face."
Isekai story about reasonable guy who don't take crap from a girl? Yes please! It turns out to be a mismash of comedy, parody, and some serious action. Guy ends up saving 2 girls from being raped and thus they start adventuring together. With God's blessings and experiences from his previous life under his subconsciousness, guy kicks serious ass and saves his party time and again. But despite being flanked by 2 beauties, he don't have any romantic interest for either and stonewalls their advances. Repeatedly and desperately holding on to his chastity.
Mushoku Tensei: Jobless Reincarnation
I have bought some manga volumes of this. Adult Japanese NEET gets overrun by a truck and is reborn in fantasy world. Remembering his past miserable life, he decides to do better this time around. He has talent for magic, and his parents hire a pretty demon instructor to educate him. Largely slice-of-life with some romance and action, this is pretty much average in isekai genre.
Death March to the Parallel World Rhapsody
Anime is available at least on Crunchyroll. Japanese game developer falls asleep under his workdesk and ends up dreaming (?) of being inside the RPG he is working on. Soon enough he is surrounded by enemies and he ends up using limited mega über attack he had coded in the game the day before. As a result of hundreds of kills, he ends up with a large amount of experience points which makes him totally overpowered game character. Because he don't feel like conquering the world, he introduces himself as traveling merchant. He also ends up with whole bunch of pretty slaves, and one of them is reincarnated Japanese. All his slaves are eager to serve their master, but instead he makes visits to brothels. HAIL TO THE KING, BABY!
Re:Monster
Originally light novel (or Web novel, whatever), I've got couple manga volumes in English. Man dies and is reborn as a goblin. However he inherited some supernatural powers from his past life he already had back then. Along with his superior human knowledge, he becomes top-goblin soon enough and leader of the tribe. With his new-found authority, he liberates captured human women from his tribe and they become his willing lovers. Spoilers tell he will have children. HAIL TO THE KING, BABY!
How a realist hero rebuilt the kingdom
Translated light novels are available for Kindle and I have read them all, short of the newest one. Japanese university student is summoned to fantasy world under attack of a demon king. Human king calls him a hero, ask for his help, and why would a hero from Japan refuse? Even though kingdom in question isn't in direct confrontation against demon lord and his minions, economy is in shambles, king's authority is undermined by corruption, and pressure from surrounding nations just keeps building up. Japanese hero has proper education for many of the problems, and therefore king declares the hero as his successor and betrothal to the princess, effective immediately. Jaws hit the floor. On top of that, princess tells the hero king to take more wives calling it a king's duty. Very unique take on isekai genre. King even kiss the princess, embrace his entire harem, and ... HAIL TO THE KING, BABY!
Aah, that took some time to type.