This is is/was discussed in some other threads but figured it was worth making anyway, hopefully is okay.
Dragon Quest was originally released on the japanese Famicom on May 27th 1986, and today marks 30 years since it's landmark release, the original Dragon Quest is one of the most important and influential titles of all time as the model most JRPGs were to follow; while elements in the game were in itself inspired by by western RPGs, the combination of gameplay elements established it as THE template for console RPGs to follow, if you like more or less any JRPG, Final Fantasy, Megaten, Pokémon, Earthbound, Persona, Tales of among many, many others all somehow borrow from Dragon Quest.
The game plays as your standard JRPG, you battle monsters, get experience and money to power up and buy better gear to fight stronger monsters, all while exploring a world full of dungeons, cities and NPCs to talk to, standard stuff, what's not entirely standard is that there's no party, you play as a loner badass on his quest to save the world, as you're a one man army you only fight enemies one at a time which makes most battles last 1 to 3 turns, get used to hearing the first few seconds of the battle theme many times!
As far as story is concerned, it's about the Dragonlord's quest to take over the world, to do this he kidnapps the daughter of the king of Alefgard to keep him at bay, with no other option the king request the help of a naked guy that fell from the sky to save his daughter, and the world.
The game however has not aged well at all, and if you haven't been playing RPGs for over 20 years (maybe even if you have) the game feels tedious, archaic, slow and even borderline unplayable. At the same time however it being such an important title is one everyone should play at least once, so briefly, here's a rundown of all versions of the game.
As mentioned before the original game was released on the Famicom in 1986, it was also released on the japanese MSX that very same year and on the american NES on 1989 under the name Dragon Warrior.
Unless you're a hardcore RPG player you're better off skipping this version (and in general all 8bit RPGs not named Sweet Home) as this as archaic as an RPG can get.
If you're in Japan or into importing the Famicom copy can be obtained at a reasonable price while the MSX is a collectors item, it's both rare and expensive, same (although not as much) can be said about the NES version.
Dragon Quest was remade alongside it's sequel for the Super Famicom in 1993. This version was never localized and it's unlikely it ever will, however there is a pretty good translation patch online.
If you don't have a problem with emulation I highly recommend getting this version.
In 2000 the Super Famicom remake saw a version on the Game Boy Color, once again alongside it's sequel, this version however saw release in NA, once again called Dragon Warrior.
This is my personal favorite version of the game as it's the most streamlined of all (saying this having not played the mobile port), also it saw an official release which isn't all that rare or expensive. Also if you don't live in NA and want to play this game remember that the Game Boy Color is not region locked.
On the final release on dedicated devices, the entire Loto trilogy was released on Wii to celebrate the series 25th anniversary, once again, Japan only.
I haven't played the mobile port so can't comment on that, but will recommend as it seems based on the SFC remake and DQ is a game that would translate well to touch controls, also it's available everywhere, that makes it the best way to play for Europeans.
To end things some videos.
CG intro of the Wii Collection
A great review of the GBC remake
TV commercial for Dragon Warrior
Dragon Quest has a great remake, can't forget about that!
https://www.youtube.com/watch?v=STahp4WPCKE
https://www.youtube.com/watch?v=IYfZJnglWtQ
https://www.youtube.com/watch?v=qk-wzULTbC4