I guess I have to emphasize that I'm not really into anime in general. I've watched only three or four series and up to a dozen films. There are things I appreciate in them but unfortunately even after so small sample they seem to be at least as cliched as Hollywood movies (cliches are little different though so at least the first series I watched, Zettai Karen Children, felt fresh).
I plan to watch more anime at some point but it's pretty hard to figure what. At the moment the only two on my watchlist are Urotsukidōji: Legend of the Overfiend (which I already have) and Elfen Lied (which I need to find somewhere).
Like in Japanese live-action film there is great variation in anime/manga. Actually manga has so much variation in style and theme that a Japanese scholar even said it was more varied than literature itself (there is manga ABOUT anything, they even adapted into manga a lot of western literature). Anime is more restricted than manga but still is quite diverse.
It is true that most anime is aimed at younger audiences and features young characters but there exists a lot of stuff exclusively aimed at mature adults that does not feature the tropes common in teenager anime. These series and movies below are good examples:
Hyouge Mono (2011) a very sophisticated series about a middle-aged lord in late 15th century Japan,
Space Brothers (2012), about two brothers in their 30s who are pursuing a career as astronauts, and
Monster (2004) about a divorced Japanese doctor who is living in Germany and is in pursuit of a serial killer that he had saved in a surgery 10 years before (and he didn't know he was "evil"). There is also
March Comes Like a Lion (2017) a drama about a shogi (Japanese chess) player and
Haibane Renmei (2002), an art-series that although features young-looking characters who behave in a "cutesy way" it mostly avoid any other cliches (and is my favorite anime of all time, over even Miyazaki's stuff).
There is a recent anime film called
In this Corner of the World (2016), about the daily life of a Japanese housewife in WW2. It is the best-animated film that I watched since Spirited Away. Other nice movies are
Millennium Actress (2002) and
Tale of Princess Kaguya (2014).
I noticed from going to conventions that Western fans of anime tend to be young and they watch only the teenager stuff. So, in the West we get a very biased viewpoint of anime/manga. A huge amount of adult anime/manga that is very popular in Japan is not even translated because it does not appeal to teenagers or otaku.