If you don't "get" anime, keep in mind that talking about anime as though it were a genre is pretty misleading -- that's like talking about video games as though they were all the same.
Now, I don't get video games, so I'm not saying you can't just not get anime, but just saying.
Anyway, before you give up on anime, try
Princess Mononoke -- and if possible, watch it in Japanese with English subtitles (or the language of your choice, I guess). The much-ballyhooed English dub with Gillian Anderson and Billy-Bob Thorton is actually rather poor, and the flatness of the voices detracts a great deal from the story.
Which is one of the more complex and thoughtful stories you'll see on the big screen.
If you don't like
that, then give up on anime. I won't complain.
The other thing about Mafia stories is they have built-in drama. For these people, their daily work is life and death, so there's lots of drama in their lives, and so they are natural subjects for stories. It's like cop shows or courtroom suspense -- natural drama.
Same thing with romantic comedies -- you're watching to see HOW they get together, not IF they get together. I love a well-done romantic comedy.
There aren't any genres I dislike, as far as I know. I just dislike movies that do whatever genre they're in poorly.
But movies I don't get are legion. And pretty much equal to movies I don't like, so that's not so interesting a discussion.