Ys Origin is 700 years before Ys 1 & 2, & leads directly into 1 & 2. It's more of a dungeon crawler, as it takes place entirely in Darm Tower, which, in this game, is more of a creature of chaos, as every few levels has a different theme, & it's stated in the story that the different levels are constantly changing(ala Castlevania). It's very fun, & for an Ys game, has quite alot of story. Plus, there's 3 different characters to play thru as, with their own stories. There's probably a Vita version in the works, but for now, it's avaiable in english via Steam.
Ys 1 & 2, as stated, millions of versions. My favorite currently is known as Ys Chronicles, & is on the PSP & PC as such.
Ys 3(takes place after Ys 4), many different versions, but they're all the same, though, I think it's the SNES version that is closer to the original names, places, etc. In otherwords, Demanicus is not the name of the final boss in the Jp versions of the game, he is known as a Galbalan(which ties heavily into Ys 6). And I think the country in the Turbo & Genesis versions is called Kenai, but it's actually known as Felghana.
Oath in Felghana is the wonderful remake of Ys 3, expanding on the story, including making Lord Macquire(sp?) a Romun vassle or something, & Felghana some sort of province of the Romun Empire. In general, the story is now very much connected to the rest of the games as opposed to the original Ys 3, which was totally self contained. Also the gameplay is heavily reworked to feel more like an Ys game IMO, partially due to it being an overhead view rather then a side scroller, but also the gameplay in general is a smoother. To me, it play's as smooth as silk, & in general is usually still considered the best Ys released thus far, even though Origin & Seven were released afterwards. Besides the PSP, you can get it on Steam, though, the PSP has some extra stuff & voice acting.
Ys 4, there's actually 3 versions, with a 4th being released soon for Vita as mentioned. It seems like Dawn of Ys was cannon originally, with the anime directly based off of it. The 3rd game mentioned is the PS2 Mask of the Sun: A New Theory. It was made by Taito, & is very different then the SNES game, & is generally considered utter trash. I've beaten it....it was ok.....I guess. The 4th game coming out in a couple months looks to be taking bit's & pieces from Dawn & Mask. The artwork deffinitly looks more like Dawn, & also there are character's in it(such as Leo) who are only in Dawn.
Ys 5 & Ys 5 Expert. I really know next to nothing about it, since no english patch has been released for either. I know it's very short & easy. I'm certain there will be a remake of it someday, hopefully it will be greatly expanded on.
Ys 6 Ark of Napisthtim. It actually was called Ys 6 in Japan, but Konami took out the 6, so as to keep people from thinking they need to play the rest of the series to understand it. Storywise, it has it's closest ties to Ys 2, 3(Oath in Felghana), & 4(due to the Romun Empire & Clan of Darkness references), & mildly to Ys 5 with Terra & her father being in the game from time to time. It's a great game, but, not as good as Oath or Origin(of which all 3 use the same game engine).
Ys Seven. Only on PSP, & Chinese PC so far. For now, it seems like it doesn't connect alot to the rest of the series, but, I have a funny feeling it's going to connect very closely to the upcoming Ys Celceta(the Ys 4 remake for Vita). Great game, uses a different engine then Ark/Oath/Origin. There's no jumping/platforming, making it, in some ways closer to the original feel of 1, 2, & 4. There was a document found that stated Ys Seven was going to be a multi-platform game. The Chinese PC version is a port by a different company, so, it remains to be seen if that falls under that category, or if there'll eventually be a PS3 version or something. I personally hope there is another version on PS3 in the works, as long as they keep it old school.
Also, there's Ys Strategy, which is NOT by Falcom. It was made before Origin was made. It's a prequal to Ys 1, but, it's just a terrible game(though, with good music). Most people call it Ys Tragedy.