Dunno what you might expect with obscure or niche, but if you're fishing for random non algorithm suggestions on something you could watch, I'll give you this: Fantastic Planet (1973)
I dunno about obscure but I owned Meet the Feebles on VHS.
I saw it in the cinema, my girlfriend was not impressed but I was already a Peter Jackson fan, so I had some idea what I was getting myself into. Talented guy, pity he never made it big.
I feel I can't recommend it - if they hate it, they'll wonder what kind of maniac I thought they were; of they love it, they'll become worried I might be able to see into their dark soul and try and so they try and kill me. Greasily.
You get it! Sadly the star Michael St. Michael was recently ill and had a GoFundMe, but that did give us the opportunity to view the movie in a limited support screening to help him out. Was worth it to see it again in theater.
Six-String Samurai, imagine if Elvis was literal King of Las Vegas, dies and leaves a power vacuum that send numerous baddies on a mission to become king, and Buddy Holly can not only play the axe, he can handle a katana blade even better. In hindsight this could just be a fallout movie with a few tweaks.
Honorable Mention: Wild Zero, very loud Japanese punk band Guitar Wolf takes on zombies with their instruments and maybe some magic?
Honorable Mention 2: Delivery, a pizza delivery driver is shit on constantly by everyone around him until he snaps and basically kills everyone who fucks with him.
The Red Elvises have Six String Samurai official full movie on their YouTube channel. They appeared in the movie and provided the soundtrack, or at least most of it.
The Tune (1992) by Bill Plympton is definitely an experience.
Hausu (1977) is a weird fever dream.
Dead In the Water (2006) was co-written & directed by a friend and is a decent indie zombie movie. It was fun seeing his parents cameo as zombies and then have Thanksgiving dinner with them.
It wasn't popular and it took forever to get on DVD, while also being an hysterically dark take on reality TV. No idea why it didn't end up a cult hit.
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.
No one I know has ever seen this movie. Dave Foley, Darrel Hammond, and uh... Steve from Blue's Clues... in a delightfully weird vampire office comedy.
Begotten is probably the most inaccessible I've seen. Least known I used to do some 48-hour film festival we'd watch everyone's in a local theater at the end and most of those never get a general release so any of those are the least available or seen. Most indies I'll watch these days are horror or drama movies. One of my favorites is the man from Earth not exactly underground but definitely under most radars.
Went to school with the writer/director, so it's fun for me picking out all the landmarks I recognize. But it's also a commentary on the play on words of the title. And who doesn't love a gory zombie movie?
Dogman: https://www.imdb.com/title/tt6768578/
Italian movie about a meek dog groomer. My friend and I still quote “SEE-MOE-NAY” to each other at least once a week.
Garage Days is a 2002 Australian comedy-drama film directed by Alex Proyas and written by Proyas, Dave Warner and Michael Udesky. Garage Days is the story of a young Sydney garage band desperately trying to make it big in the competitive world of rock music. Its soundtrack includes the song "Garage Days" composed by David McCormack and Andrew Lancaster and performed by Katie Noonan. The climax of the film was filmed at the Homebake festival in Sydney in 2001.
Of Unknown Origin (1983). A man becomes destructively obsessed with killing a dangerous rat, which has taken residence in his recently renovated house.
I remember watching Evil Bong (2006) because it was included in a 10-movie horror bundle in a Walmart bin. I don't know how niche it is, but none of my friends have ever seen it before showing it to them.
I can't say it's worth watching, but it certainly exists.