Gundress (1999) is the most obscure anime movie I've seen and maybe also the most obscure movie overall -- of stuff that was actually professionally made and shown in theaters, anyway. I posted about it in one of the weekly anime threads a couple months ago with some screenshots and additional details.

Outside of anime, I've seen a number of cult films and non-English films that are probably obscure to English speaking audiences, but I have no idea how obscure they actually are. (The one above I know is obscure since it doesn't even have an English Wikipedia page -- unlike every other anime show and movie I've seen.)

Some examples are Wonderwall (1968) with music by George Harrison, eXistenZ (1999), Cemetery Man (1994), and I Served the King of England (2006). I know at least one other person on Lemmy has heard of Cemetery Man since it was brought up in a thread around Christmas, but they were surprised I'd seen it.

Primer (2004) and Dark Star (1974) also came to mind, but I don't think those are actually that obscure. They are interesting though.

Edit: rephrased for clarity

Edit2: typo in title fixed ("Kind" -> "King")