There are some gold nuggets within the genre/medium that are worth watching even if you despise typical anime.
If you're like me and loathe a lot of the overused tropes and clichés that define so much of mainstream anime (teenagers, school uniforms, derivative plots, annoying hair, annoying personalities, annoying angst/adolescent bullshit, annoying over-the-top animation/"kawaii" and so on) there are still quite a few decent ones out there that either sidestep these tropes all together or somehow rely on them sparingly/in reasonable amounts. That's because they're, erm, good in their own right.
That said, here's a list of anime for people who don't like anime. This is off the top of my head so I might have left out a few:
Ghost in the Shell (movie)
Ghost in the Shell: Stand Alone Complex
Akira (movie)
Plantes
Cowboy Bebop
Serial Experiments Lain
The Animatrix
Paranoia Agent
Jin Roh (movie)
Great Teacher Onizuka
Neon Genesis Evangelion (starts off slow, you have to stick it out)
Battle Angel Alita
Memories
Technolyze
...And there's probably more, but this is a solid start.
I find that a lot of people knee deep in anime fandom will recommend stuff like Sword Art Online, .hack//sign, Attack on Titan and Gantz in such a list, but I've tried watching all of these and found them to have too many in common with generic anime to be really enjoyable. I honestly don't know how anyone older than fifteen thinks Gantz is worthwhile as serious storytelling.
An honourable mention would be Ergo Proxy but I found it to be lacking as well.
Sword Art Online is incessantly praised on reddit but I think it's shit. It might be alright if you're under 20 and have never read Snow Crash or Neuromancer before, otherwise it's not much more than a run-of-the-mill anime full of typical tropes, a touch of edginess and novelty.
Also some people are probably going to say that a lot of my list is "Japanese animation" and not anime because a lot of it is cliché/trope-free. So be it.