What Aman said is true, which is why I'm finding it particularly difficult to narrow down any artists in my library into the category of "obscure." I guess the easiest way I'll be able to get close to anything truly obscure would be by naming off some lesser-known bands that are part of fairly obscure genres to begin with... here goes!
NeoFolk/Apocalyptic Folk:
Backworld - Unlike other bands in this genre (and despite being on David Tibet's label) Backworld are not your typical post-Industrial, traditional European Folk inspired group. Rather, their music is very relaxed and laid back, peaceful melody laden acoustic driven forays that only dabbles into the common themes found in the genre. Very, very beautiful music; often hauntingly so. Recommended tracks: Devil's Plaything, Leaves of Autumn, The Sparrows.
Gae Bolg and the Church of Fand - Interesting martial music that ranges in sound from lively marches to neoclassical to Industrial to jigs (and even a "techno remix" of one of these jigs!). I don't know much about this band except one of the members is also involved with Sol Invictus, but there's really not that much information about them out there...
Nový Svêt - Another band I don't know that much about. Lots of different styles come into play, even across the tracks on the single album of theirs I have.
(Wow, I'm pretty bad at describing these bands... maybe I should just stick to name-dropping...)
Lothlorien
Oraison
XIII - Only song I've heard by them is a cover of "Black Easter" found on a Sol Invictus tribute album. It is unbelievably good.
No Wave:
Dark Day - Former member of DNA R. L. Crutchfield's project. Has a similar vibe to DNA but is not as atonal or noisy. Emphasis is on synthesized and unusual instruments.
Noise (hard to describe any of them in words, if you're familiar with noise you already know that most artists try to explore the most extreme reaches of sonic territory, you must hear it for yourself):
C.C.C.C.
Dead Raven Choir
Wold
Concrete Violin
Other:
Space Machine - A side-project of Yamazaki Maso (aka: Masonna). Imagine floating around in space and being able to hear meandering signals and waves of unknown origin as they come and go, meandering through the infinite void.
Christine 23 Onna - Another side-project of Yamazaki Maso, except this time he's teamed up with the guitarist from Angel'in Heavy Syrup. The result is a psychedelic trip similar to a stripped-down version of Acid Mothers Temple with an emphasis on groovy guitar riffs and spacey electronic noodling.
Moonn D))) - A Sunn O))) cover band... imagine that!
Napoli Is Not Nepal - Mostly relaxing, albeit somewhat glitchy, ambient electronic music.
The Kallikak Family - I've tried describing this band before and failed, so I won't try again. A lot of electronic sampling and stuff going on, as well as cool guitar phases and such, all with a very depressing vibe to it. Some of the most singularly unique music I've ever heard.
Ok, sorry for making such an unorganized post. I forgot everything I was going to say when I actually tried to write it.