Thanks for expressing an interest in the murkier depths of my record collection. "Bafflingly obscure" is a purely subjective term, of course, but I think it's safe to say that none of the following ever troubled the top 100.
The New York Art Quartet - Same (1965)
Jazz, improvisation, poetry and race. Disproves the notion that all the mid 60's radical, free-thinking progressive stuff was happening on the west coast.
Village Of The Pharoahs - Pharoah Sanders (1973)
Bells, flutes, chants, tamburas - more great spiritual jazz.
Nosferatu - Popol Vuh (1979)
Appropriately creaky, spooky, yet oddly beautiful soundtrack to the Herzog/Kinski arthouse vampire flick.
Live, Love, Larf And Loaf - French, Frith, Kaiser And Thompson (1987)
Oddball collaboration of folkies, art rockers and avant-gardists. More fun than it sounds, with the great Richard Thompson singing a (very catchy) traditional song in the Okinawan dialect.
If'n - Firehose(1987)
Much missed (by me, at least) jazz/punk/funk/art-rock trio with a great record of short, sharp, and ever so slightly quirky songs. Oh, and Mike Watt is surely the post-punk Jack Casady. Listen to him go on From One Cums One.
The Word - Jonas Hellborg (1991)
Virtuoso acoustic bassist, backed by a string quartet, and late, great drummer Tony Williams, who mostly sounds like a six-armed hyperactive child trying to hammer his way out of a locked wardrobe - albeit a child with uncanny rhythmic timing and stunning technical ability.
Weird Nightmare - Hal Wilner (1992)
A musical tribute to Charles Mingus, featuring the home made instruments of Harry Partch,and a truly eclectic cast featuring Keith Richards, Charlie Watts, Vernon Reid, Bill Frisell, Diamanda Galas, Robbie Robertson and Elvis Costello, amongst others.
Miracle - Bim Sherman (1996)
Smoky, soulful vocals set against a backdrop of acoustic guitars, tablas, and an Indian string orchestra to create something life-affirmingly mellow, and so utterly gorgeous, it would even melt Dick Cheney's heart. (Probably).
Jazzactuel - Various (2001)
"A collection of avant-garde/free jazz/psychedelia from the BYG/Actuel catalogue of 1969-71"
Says it all, really. With Steve Lacy, Archie Shepp, Gong, Daevid Allen, and a monumental piece from Alan Silva. Triple LP.
The Lark Descending - Chris Wood (2005)
Beautiful contemporary English folk. Genuinely great songs.
Like Love, Lust, And The Open Halls Of The Soul - Jesse Sykes And The Sweet Hereafter (2007)
Lovely laid back country/folk/rock with a nice 70's vibe.
Alone In The Dark Wood - Fursaxa (2007)
In which a one-woman band performs what sounds like a peyote-fuelled shamanistic ritual in the desert at night, while coyotes howl and prowl in the surrounding darkness. Those people discussing the meaning of psychedelia elsewhere on this forum may care to check this out.