Ys I is a great game and fully playable in DOSBox. It can be obtained for free from many Abandonware websites. For example:http://www.abandonia.com/en/games/860/A ... of+Ys.html
There is also a Steam version of Ys Origin.
Another DOS JRPG worth checking out is Zeliard. It was developed by Game Arts, the same folks responsible for the Lunar games:http://www.abandonia.com/en/games/957/Zeliard.html
I highly recommend Falcom's Sorcerian as well:http://www.abandonwaredos.com/abandonwa ... n&gid=NjUx
I believe The Last Remnant has somewhat beefy system requirements, so make sure your system can run it (mine can't, so I bought the 360 version).
Final Fantasy VII, Final Fantasy VIII, and Grandia II all have PC ports - but they may be tricky to run on modern systems (keep in mind they were released during the Windows 98/ME days).
As isiolia mentioned, there are several "JRPG-ish" games made by Western developers for the PC. Septerra Core and Anachronox are the two biggies. The former can still be found new (check Amazon) for about $5, try to get a newer version with Windows XP compatibility. Anachronox is a bit pricier.
There are also some quality (Western developed) RPG Maker games that imitate the Final Fantasy/Chrono Trigger aesthetic pretty well. Lots of these are free, some will cost $10+. I recommend the Aveyond series.
In all honesty though, you're much
better off getting some emulators if you're looking to play JRPGs on the PC. Start with something like SNES9X (a SNES emulator), which is very user-friendly and should run on any modern day computer. Lots of classic console JRPGs were completely turn-based and thus fully playable with a keyboard - Breath of Fire I + II and The Seventh Saga come to mind. For action-JRPGs (Secret of Mana, etc) I would recommend getting an actual SNES controller along with a Super SmartJoy (USB converter).