So, thanks to my music explorations here at SDMB, I found the band Anubian Lights and the DJ Cheb I Sabbah, both of whom are a sort of mixture of electronica and Middle Eastern music. I also like Suba, who mixes Brazilian music and electronica.
Any suggestions of other bands like these?
Popol Vuh, the originals.
If you want something from wayyyyyy out of left field, you could try Back Tuva Future. It’s not all electronica, but it is all Tuvan throat singing 
Just downloaded their most popular song on Itunes, and I like it. Thanks!
Shpongle. Trippy as hell, but too weird for a lot of people. Give it a chance though.
Try out “Karma” by Delerium and the self-titled debut from Conjure One.
You might like Agricantus - the lead singer is Swiss and comfortable singing in several languages; much of their stuff has an African & Arabian influences.
There’s some stuff by Thievery Corporation you might like as well, but probably not all of it.
Afro-Celt Sound System. Pretty self-descriptive.
I’m fond of the Buddha Bar compilations.
Came to recomend Thievery corp as well, one of the greatest bands I have ever seen live. they tour with 5-9 different singers who sing a wide variety of different styles of music from around the planet all backed by a mix of live instruments and 2 dj’s
The Ozric Tentacles
Usually quite upbeat and rocking, so it may not be what you’re looking forward.
Erpland (album) would be a good starting point.
Bally Sagoo, Natasha Atlas, Transglobal Underground. I second the Buddha Bar comps as well.
The album Hibernia, by Dagda, is pretty interesting. Electronica, folk, ethereal b.s. (that’s a technical term, apparently ;), it’s got a bit of everything smushed together.
One of my favorite ambient/electronica groups is Uman, a French brother & sister duo.
I was going to say Niyaz, but Yookeroo beat me to it. I’ve been listening to their CD over and over since it came out, their Sufi groove has really captivated me. My wife is from India, she knows the song “Allahi Allah” from her childhood because it’s a folk song everybody sings over there. She sings along with it.
I love everything by Natacha Atlas. Great voice, good choice of grooves, she’s got everything. She is connected with the Transglobal Underground, which is all about merging world/electronica. Her music is really sexy but also with a spiritual touch.
The whole series by dj Cheb i Sabbah including Shri Durga (classical Hindustani vocals) and La Kahena (North African/Arab/Sufi/Jewish) is outstanding. IMHO.
Cheb i Sabbah worked on that series with Bill Lasswell, who was also responsible for Aisha Kandisha’s Jarring Effects (named for a notorious legendary cave demoness of Morocco), one of the early electronica/world efforts and well worth a listen. Lasswell has done tons of experiments in merging world and electronica.
My Life in the Bush of Ghosts by David Byrne and Brian Eno was the album that invented the idea of electronica world in the first place in 1981, it has since been reissued.
My brother has a cd by this band called Ivan Kupala that puts Russian folk music to electronic beats.
You can listen to some samples on their website. It’s in Russian, but you can hear the samples by clicking the song titles. I kind of like the samples for the second and fifth songs on that page.
I was gonna suggest them too.
I dunno, maybe Soap Kills ? They’re sort of electro-Lebanese.
Should I assume you’ve seen the anthologies from
http://www.putumayo.com/ ?
The Idan Reichel Project. Reichel combines Israeli music, Ethiopean music and electronica; his stuff was top-10 here in Israel, so you’ll probably find it pretty accessable. Check out the audio samples in my link.