Ok, I've brought this up a couple times, so it's high time I actually discussed it. The basic principal of tribal metal is really quite simple: it's folk metal where the "folk" part is Native American. So, really, it's just a different type of folk metal. I choose the use the "tribal" title for two reasons. One is that it helps to keep things clear, since when one says "folk metal", something European is usually expected. The other is that, quite simply, I think it sounds cool so I relish the opportunity to use that name. Another name sometimes used is "native metal".
Anyway, there is a good spread of tribal metal from throughout the Americas, though it's found primarily in South America and Mexico. There is also a interesting niche of more electronic sounding tribal metal to be found in Europe, particularly Russia and Germany.
I've actually found a Youtube video that gives a pretty good sampling of bands from the Americas, which I'll link here.
The bands included on this sampling are:
Gnosis (there are several bands with this name)
Soul of Honor
This sampler plate will give any interested listener a starting place, but my personal recommendations for full albums would be EK's 2005 self-titled release, or either full-length by Yaotl Mictlan. Most of Yaotl Mictlan's material is more of a straight-forward black metal sound, so it may make for an easier transition. Two other bands who don't appear on that video but who are worth checking out are Kukulcan and Yanaconas. Kukulcan has a pretty rough, low-fi sound rooted in black metal, while Yanaconas has more of a traditional heavy metal sound.
Kukulcan - Señor de la guerra Huitzilopochtli
Yanaconas - Tupac Amaru
Yaotl Mictlan - Garra de Jaguar (Ocho Venado)
As for the European "scene", the two primary bands worth listening to are Tenochtitlan and Raxa, both from Russia. These bands, as I said earlier, both feature far more electronica than is typical in the tribal bands from the Americas. Raxa in particular, though, has some really beautiful sounding tracks, and I would strongly recommend their 2008 release MezoVedic. Honestly, I personally prefer this to any of the "authentic" tribal metal. As a side note, Senmuth from Tenochtitlan has an individual discography that dwarfs virtually anything else you'll find on the Metal Archives.
Raxa - Matenextic Peuhtica
One other band that is tied to this niche but is a little too eclectic to really fit neatly is the fantastic SpiRitual from Germany. In my previous, quickly aborted blog I discussed SpiRitual in more detail. That can be found here.
If you don't listen to anything else off this list, I would strongly suggest that you at least check out Raxa and SpiRitual. But be warned that there are often long mellow periods to be found in their songs, so if you prefer more aggression steer clear and head for Yaotl Mictlan instead.