I'm sorry, right now I can only think of the old Shining Force or Phantasy Star titles (too many games have real-time components or overly cute/child-like designs nowadays ), which you could buy as the Sonic Ultime Genesis Collection .

I'll post again if I remember some newer game that fulfills your criteria.

Yeah, I know SF and PS. I hope you will remember a somewhat modern game like that. :)

Xenosaga series maybe? Haven't played Xenosaga myself but the series looks good and "epic" and they were made by people who worked on Chrono Trigger/Cross and Xenogears. Btw, if you don't mind PS1 games then try Xenogears :)
Oh, and Valkyrie Profile 2 (again, if you don't mind PS1 games then Valkyrie Profile 1 as well). It's an epic game with an epic story and epic characters. It also has a more mature feel than most other JRPG's. The battle system is turn-based but you can move characters around on the battle field.

And I agree with Soriku, Baten Kaitos is totally worth it.

Suikoden II. If you hate that then I will have lost faith in humanity.

Xenosaga looks interesting, thanks for the tip. :) As does xenogears, but I think I would like to try some newer games first.

And that could be the most annoying thing on jrpg:s ever. I don't want to play a chess match every single time there will be a random encounter. No. No way. NEVER!

Don't know about that one. Looks like anime to me.

Once you've played FF X, all future JRPGs just can't measure up...(imo)

SUIKODEN fits the bill, epic stories, turn based combat etc.

Grandia is another one you can check.

Yeah. That could be true. I think Lost Odyssey is the closest match to FF X though.

Which Suikoden and Grandia? Does those games have real turn based battle systems? :P