I'm not going to enter the debate of how celtic Celtic Metal is (ok, maybe just a little) but for me the name Celtic Metal designs bands with more or less strong links to the Celtic culture, they aren't exactly Celtic. Putting a specific genre on a band is also a way to give someone an idea what they should expect from a band. The name is often take from a detail in said genre, for example the name of the black metal genre comes from a Venom album, this doesn't means that every black metal recording has exactly the same sound as this Venom album (luckily!), in the same way I think that a metal band of the Celtic metal genre doesn't necessarily needs to be 100% Celtic. Classifying a band is also no exact science so of course not everyone can agree.

Now to add my 2 cents to some of the great bands I have seen listed here, of those listed Falkenbach and Eluvetie are my favorite, I'd also list Primordial.

Also give Heidevolk, Myrkgrav, Ulver (the first three albums) and Helrunar a try if you like this kind of music, they're more Folk and Pagan/Black metal, but hell I'll still list them anyway.

If you want to learn something about a metal band go check www.metal-archives.com, however they don't list grind, hardcore, metalcore, neometal and hardrock (of course there are exceptions) *** they have to draw a line somewhere on what is metal and what is not.