A simple request, I hope. Anything, really - the odder the better. I’m in a mood for being open-minded. (Downloadable stuff would be great 
)
Anything by “Art of Noise”. Especially from the early to mid 80’s.
You asked for it! The work of Conlon Nancarrow springs to mind straight away.
Another quicky, go and look up the Gamalean(sp?) Monkey Chant
I’ll see what else I can think of.
Google is my friend, first result on “Monkey Chant”:
Download the Monkey Chant!
The Monkey Chant is kind of interesting…Art of Noise? Pffft. And I’ve already got most of Nancarrow’s recorded stuff.
Come on guys, you can do better 
:wally …
How about some Khanate, Earth, or SUNN 0)))? Maybe Ulver’s Nattens Madrigal? Or Arcturus’ The Sham Mirrors?
Merzbow’s an old favorite, but that’s not really music, per se…
OK you’ve got Nancarrow. Have you heard Eight Songs for a Mad King by Peter Maxwell Davies?
Heard of [The] Verve? Get their first album, A Storm In Heaven. It sounds nothing like you’d expect it to, it’s pretty unique.
My regular pimp for weird stuff:
http://www.epitonic.com/artists/paulineoliverosstuartdempsterandpanaiotis.html
Ken Nordine’s Colors (Amazon has samples from all of the songs).
Of course, Re/Search’s Incredibly Strange Music vol. 1 and 2 are classics (and one contains a song by Ken Nordine).
There’s also that “singing Jesus dog” album out there with a song on the website… (I’m blanking on what it was exactly but the cover has a blonde woman with her dog and on the back it’s the dog at a toy piano).
You can’t go wrong with the Thai Elephant Orchestra - that’s right, it’s actual elephants playing gamelan and gongs. It’s actually really subtle and even pretty.
Also, there are two long out-of-print compilations out there called Incredibly Strange Music volumes 1 and 2. It’s a comp of really out there proto-exotica and novelty songs, and some of it’s downright disturbing.
Also, you can’t go wrong with Bruce Haack, who built his own synthesizers and made bizarre, synthesized children’s music. The Hush Little Robot compilation is always a great starting point.
I don’t count it as music, but Mike Patton’s Adult Theme For Voice (there are samples available here) is…well…a grown man making exceptionally weird noises into a microphone.
Ween is pretty good for just weird too…
I’ll suggest the doyenne of Romanian folk music, Maria Tanase. I ran across a record of her 40’s recordings years ago at the Boston Public Library, when I was just browsing for music I’d never heard of, let alone heard. I still think she’s pretty remarkable – a husky voice that travels from whispers to shouts, backed in many cases by a semi-frantic orchestra.
You can get mp3’s of some of her songs at http://cristian.francu.com/Maria.
Check out #5, Cand Toca La Radu Voda a slow ballad with the aforementioned semi-frantic orchestration,
I’ll suggest the doyenne of Romanian folk music, Maria Tanase (1914-1963?). I ran across a record of her 40’s recordings years ago at the Boston Public Library, when I was just browsing for music I’d never heard of, let alone heard. I still think she’s pretty remarkable – a husky voice that travels from whispers to shouts, backed in many cases by a semi-frantic orchestra.
You can get mp3’s of some of her songs at http://cristian.francu.com/Maria.
Check out #5, Cand Toca La Radu Voda, a slow ballad with the aforementioned semi-frantic orchestration, #10, Cintec de Leangan, which might be either a lullaby or a lament, #15, Cat li Mamamuresul, which is apparently a Romanian trudging-song, and #20, Ciuleandra, a dance that starts off slowly and ends up rollicking. All of these, as well as some of the others, seem to be of 1940’s vintage. Some of the songs on the site that I’d guess were recorded in the early sixties sound sanitized, as though she’d lost her youthful edge. (My apologies for the above ssentence’ss alliterations!)
Not understanding Romanian won’t necessarily hurt you here, not that I’m presuming that you don’t, of course. After loving some of these songs for years, I did some digging on The Internets, and discovered that she often sang about potatoes, winter weather, and weeds. But I find her to be a passionate and emotive singer, not to mention wonderful to drink by.
Another CD I put on a lot when I’m wanting something unusual is The Slits’ Cut, from 1977. I had it on vinyl when it first came out, lost the record and was left with a crappy tape-dub until I found it on CD on amazon a couple months ago. God how I still [heart] these girls!
I’m sorry, there seems to be some problem with the link above. I can access from my favorites, but not from the post. Deeplinking trouble?
And I don’t know why there’s half a post above the full one.
I’ll go away now…
I trust your good taste enough to presume that you’ve already heard Zappa, Captain Beefheart, Wesley Willis, and the Shaggs.
So I think I’ll recommend most of the stuff on this page, especially the stuff by the Ruins (listen to Praha in Spring NOW; you won’t be disappointed), Shakuhachi Surprise, the Space Streakings, and the Flying Luttenbachers. People Like Us and DAT Politics are two of the more interesting electronic musical entities out there. A lot of the stuff in the Experimental section of epitonic.com is pretty good, and almost all of it is interesting in some sense. As for stuff happening near me that I’ve seen live, Alec K. Redfearn’s projects are great if you’re into Eastern European-influenced accordion rock.
A few random thoughts on stuff that I’d consider weird…I don’t know whether any of these are downloadable.
Throbbing Gristle.
Chrome. Also Helios Creed’s solo work.
Acid Mothers Temple.
The Damo Suzuki Network.
Tuvan throat singing.
Johnny Dowd.
The Trachtenberg Family Slide Show Players.
An album called “Laments” put out by the Finnish Literature Society (this is an ethnomusicology collection of joik-singing laments from Karelia)
Another album from the same publisher called “Kelkettelyeanija Eli Vienankarjalaisia Joikuja” (more ethnomusicology)
Another album from the same publisher called “The Kalevala Heritage” (more ethnomusicology, this is recordings from the early 1900s of the songs that helped make up the Kalevala)
An album by Koyhat ritarit and PRIMO (The Poor Knights and the Primitive Music Orchestra) called “Karhujuhla” (this is a presentation of an ancient Finnish bear-hunting song cycle)
Baby Gramps.
An album called “Im Silo, Alte Musik - Neue Improvisationen” (this is a binaural recording that was recorded in, well, a silo)
Pauline Oliveros.
The Residents.
Clock DVA’s The Connection Machine is pretty bizarre. You might also want to check out the suggestions in this thread.
There’s also this site.
The Polyphonic Spree - pop music, with a full orchestra. Sort of.
Also http://www.stark-effect.com/ (and the links page on that site)
I recommend “Green Eggs and Ham” and “The Archaeopteryx” – read the explanations of how they made them, and you might appreciate them more.
V/VM are a group of remixers that take pop tunes/classics and do…things with them. They have a range of downloadable tracks/samples but I don’t hace the link on this computer - check out what they do with Shostakovitch - its 5 or 6 of his symphonies all playing at the same time, which sounds better than you might expect.
I’ll second The Residents too.
If you can find ‘The Elbow is Taboo’ by Renaldo & the Loaf it’s unusual, but also kind of like death by musical laughter. Its the most pretenscious record ever made, but still fun.