OM has released the album of the year for me (Advaitic Songs), and it's some of the best music I've ever heard.
The eastern-meets-doom-metal sound they have is very unique. Really bass heavy, a thick smoke kind of sound (I can imagine smoking hookah to them),
and of course the eastern/religious vibe. Is there anything out there like them
For anyone who needs a sample, here is some from their latest album.

http://youtu.be/3uF3x_MBEa4
http://www.youtube.com/watch?v=R2WzZnUefCc

EDIT - Just heard some of the solo stuff from Karl Sanders and I love it. Only have Saurian Meditations, but is there any other music out there similar to his Ancient Egyptian style music?

Basically, anything exotic/foreign influenced music? Would prefer if it's made from metal musicians, but open to anything.

Nothing?
Not even stuff similar to Natural Snow Buildings or Six Organs of Admittance?
Anything would be appreciated!

I havent heard much else that could compare to those two bands but maybe you will dig Wreathes. Definate eastern sound to it, almost chant like vocals.

http://wreathes.bandcamp.com/album/wreathes

Two members of wreathes are also in a band called Kinit Her. They are much more experimental but check them out too. The burial hex split called Vedic hymns would be your best bet.

http://kinither.bandcamp.com/

I think a lot of the bands comparable to this are not going to be in the Metal Genre per se. Check out more neofolk and ritual ambient bands.

Senmuth

http://www.metal-archives.com/bands/Senmuth/90703

It's too much albums, make a search on the internet of which one you should get into.

I also listen to Karl Sanders and find the (fantastic) "Atlantean Monument" album by Lord Wind quite similar in atmosphere. Not as "eastern" sounding as Karl S. but very percussive, "ancient" (in terms of evoking pictures in your mind).

Here is sth to check out:
http://www.youtube.com/watch?v=2_V6cSYjOmQ

Check out Grails, the drummer for Om played with them and they definitely got that Eastern vibe going on. They're purely instrumental, but the way I see it, they're so good they don't need a vocalist. Here's some tracks by them:
http://www.youtube.com/watch?v=r3btWND4WVA
http://www.youtube.com/watch?v=rAnbR2a2IxA
http://www.youtube.com/watch?v=g5NfwZRBrKE
http://www.youtube.com/watch?v=p3yw6897F_A

Check out White Buzz and Naam.

Naam is sort of like 60's psychedelic rock with a pretty cool vibe similar to Om.

White Buzz sounds a lot like Om. More so than any other bands I've heard.

I keep meaning to check out Karl Sanders solo stuff. But for middle-eastern sounding music, Trial of the Bow is fairly mandatory, featuring members of Disembowelment.
http://www.youtube.com/watch?v=zwBl3rYUQ6U

Not metal-related, but one of the best middle-eastern albums ever is Rabih Abou-Khalil's "Nafas" album
http://www.youtube.com/watch?v=oEuiormA2fI
http://www.youtube.com/watch?v=fDldnVaQtR8

Or maybe some authentic Afghan rubab music (sometimes spelt rabab), like this album by Essa Kassimi
http://www.youtube.com/watch?v=CqK_LECFB2E


Edit:

Or if you don't mind some far-out space/psych-rock, maybe some of Ozric Tentacles material. Guitarist Ed Wynne is a master of eastern styles.
http://www.youtube.com/watch?v=0oQJrB_caQg
http://www.youtube.com/watch?v=-2D49PNdqP8
http://www.youtube.com/watch?v=ZN6yLkFPWxk

Sorry to resurrect this after so long, but I wondered if anyone else had come across any Om-like middle eastern (or simply 'world') inspired music - be it stoner doom, or any other sort of music, really.

Loved a lot of the suggestions here, including Naam, WhiteBuzz, and the Afghan and Lebanese music mentioned above.

Everyone should definitely be listening to Ozric Tentacles, and see them live if they get the opportunity.

My own suggestion is Blaak Heat Shujaa - full album available on youtube:

https://www.youtube.com/watch?v=2YMI09im5pI

A friend pointed this out to me earlier, and its pretty darn good - particularly psychedelic and somewhat OM-esque and/or desert-like vibes going on.

Look forward to seeing if anyone has any other suggestions.

There's a band called Zaum that's heavily Om-influenced but with sitar-like sounds that makes them sorta sound like Grails. There's apparently a full length coming out soon.

http://zaum.bandcamp.com/

Check out the band Bong from the UK. They combine long psychedelic drone/doom songs with the Sitar and Shahi Baaja.
http://www.youtube.com/watch?v=VwlB_NX9npM