I want to read a really really good "transported to a fantasy world" manga or manhwa.

Like Red River or Tate no Yuusha no Nariagari. 🙂

From Far Away

[img]http://orig14.deviantart.net/cb0c/f/2012/171/4/b/gif_by_emoxynha-d549jj5.gif[/img]

This one's pretty good so far, but only has 6 chapters scanlated right now. :/
Isekai de "Kuro no Iyashi Te" tte Yobarete Imasu – An otaku girl in college gets to another world where she finds out she's a witch/maegi and kind of really powerful so she tries to help as many people as she can.
Another one is Overlord but I haven't read it yet, so I don't know myself if it's any good or not. However, everyone's been recommening it lately, and saying that it's really good so maybe you should check it out anyway?
Oh! And how could I forget about +a no Tachiichi. It's about two high school girls who are transported to another RPG like world. Good Looking Girl is seen as the "heroine/chosen one", but Plain Looking Girl is who actually has the powers/the true chosen one, but still everyone thinks it's the prettier one and Plain Girl is okay with giving another one the spotlight (and the harem), so she works hard in the shadows to keep up the charade. It's really good but really short (only 12 chapters of which 11 are scanlated already).

And also, you can check the tag https://www.mangaupdates.com/series.html?category=Transported+to+Another+World&orderby=rating to find other works with the same basic plot (transported to another world).

If I remember another manga like what you want, I'll edit to add.

Isekai Maou to Shoukan Shoujo Dorei Majutsu
Tsuki ga Michibiku Isekai Douchuu
Tensei Shitara Slime Datta Ken
Re:Monster
Konjiki no Moji Tsukai - Yuusha Yonin ni Makikomareta Unique Cheat
Isekai Tensei Soudouki kind of

He has two personalities in him from another world

Hachinan tte, Sore wa Nai Deshou!
Gun-Ota ga Mahou Sekai ni Tensei shitara, Gendai Heiki de Guntai Harem wo Tsukucchaimashita!?
Chihou Kishi Hans no Junan

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Saver and Rure are pretty similar to Red River. If you're looking for something more lighthearted, I recommend watching the anime Kono Subarashii Sekai ni Shukufuku o!, which is a good parody of the whole "transported into a fantasy world" trope.

You might like Fushigi Yuugi and its prequels or maybe The Queen's Knight.

Threads of time
inuyasha in case you haven't heard of it
drifters
world customize creator I have not read it yet but I think it might fit

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Amagoi - Year: 2009; Scanlated up to chapter 16 (not yet completely scanlated despite the manga being complete in Japan). I'd also like to note that I haven't read this but I thought it was worth adding because one of the categories is "Transported to Another World" and it's of the "Fantasy" genre.

Death March kara Hajimaru Isekai Kyousoukyoku - Year: 2014; Scanlated up to chapter 8. It says that the English publisher will be Yen Press, however, the date is yet to be announced.

Demon Spirit Seed Manual - Year: 😕 ; Scanlated up to chapter 53.

E? Heibon Desu yo?? - Year: 2014; Scanlated up to chapter 18.

Grimore x Reverse - Tensei Kishin Roumantan - Year: 2015; Scanlated up to chapter 2.

Immortal Regis - Year: 2006; Completely scanlated with 6 volumes and 44 chapters.

Isekai Houtei: Rebuttal Barrister - Year: 2016; Scanlated up to chapter 2.

Kekkon Yubiwa Monogatari a.k.a. Tales of Wedding Rings - Year: 2014; Licensed and published digitally by Crunchyroll (up to chapter 21 so far).

Kenja no Mago - Year: 2016; Scanlated up to chapter 3.

Koushaku Reijou no Tashinami - Year: 2015; Scanlated up to chapter 10.

Kumo Desu ga, Nani ka? - Year: 2015; Scanlated up to chapter 11 (though it only shows to chapter 3 because I think past that it was done by individuals rather than scanlation groups).

Maken no Daydreamer - Year: 2016; Scanlated up to chapter 3.

Ore to Kawazu-san no Isekai Hourouki - Year: 2013; Scanlated up to chapter 19.

Red Storm - Year: 2012; Licensed in English and published by SpotToon as well as scanlated up to chapter 213. The one who is transported to another world is the main protagonist's master . . . as you're looking for something where the main protagonist is transported to the fantasy world then this probably isn't what you're looking for as even the main protagonist's master himself is from a "fantasy world."

The New Gate - Year: 2014; Scanlated up to chapter 21.