I really like early Clannad, basically everything up to Magical Ring. Also Iona, they're very Celtic but with less traditional aspects such as synthesizer "soundscapes" and electric guitars and basses.
Most things folky are fine by me - I'm a big fan of Bellowhead as I may have mentioned. Okay they're not Celtic/Irish/Scottish but don't discount the English stuff, there's more to it than Scarborough Fair, though it's often passed over. Alestorm, though not "trad", are nonetheless very folky, also Jethro Tull circa Heavy Horses/Songs from the Wood. Pogues, Dubliners, Dropkick Murphys et al - I'll never complain about hearing any of that sort of stuff.