Speaking as someone who - despite what my collection may imply - doesn't care much for JRPGs, I think the Tales of... games are among the best in the genre, and some pretty great games in their own right. Fantastic music, a unique fighting system, and some wonderful plots and characters that just love to viciously turn traditional JRPG cliches on their heads. Shame that only maybe half of them were ever localized, though. That atrocious Tales of Phantasia GBA port doesn't count.
However, to be perfectly frank, I think introducing yourself to the series with Dawn of the New World (which is what I'm assuming you just picked up) will end in disaster. I personally think it is the weakest in the series, both story- and gameplay-wise. (And I'm not at all bitter because Symphonia is my favorite in the series, no sir...) I suggest trying out Symphonia, Xillia, Vesperia or Graces before anything else. Tales of the Abyss is also pretty popular, though I personally thought it was overrated. Like karyann said, each game is self-contained - with one or two notable exceptions - so you should have no problem playing them out of order. Good luck!