It's a pretty literal interpretation of what you said, but Angel's Egg has almost no dialogue while still managing to be deeply expressive. Mind Game is quite unique, as well, since it switches constantly between different art styles. If you want something really wacky, try that. Cat Soup is another great example of a story being told without dialogue, mostly through a series of metaphors and dream sequences. I've not seen all of them, but Shigeru Tamura's work probably fits into the same category as Cat Soup: Glassy Ocean, Minor Blue and A Piece of Phantasmagoria. From your Lain picture, I'm guessing you've already seen that, but make sure to check out other stuff Yoshitoshi ABe's worked on. Technolyze was already mentioned, and Haibane Renmei's got a lovely feeling to it. I've not seen any of his other stuff, but I trust my main man Y to the A B enough to know they're probably good. There's also stuff like the End of Evangelion and FLCL, but everyone and their grandmother's seen that, so it's probably not worth mentioning.
That's all I can think of off the top of my head. Will post more if i can think of any.
Maybe this isn't what you're looking for, but there's always Cat Soup if you haven't already seen it. MindGame is another one that I almost never see mentioned, despite it being one of the most unique animated movies I've ever seen.
cat soup is that trippy one with the brother kitties right? I'd say that pretty much fits OP's request.
I was going to suggest Mind Game but OP asked specifically for very experimental stuff like stuff without dialogues and the like. In that sense most of what has been suggested are pretty much regular stuff.
I guess this is a really old anime but it was one of my favorites. It's really comfy and some of the hand animated scenes blow me away. Has rotoscoping and I know that's a popular technique but it's done very well in this anime. Bobby ni Kubittake Sorry if this isn't what you're looking for.
i'd highly recommend genius party; happy machine is one of my favorite things on this planethttps://bakabt.me/torrent/146806/genius-party-bss