I'm mostly interested in shows that focus on character development, so I guess romance works for me as long as the show isn't a romcom (slapstick comedy and abrupt tone changes really sour me on shows). It's probably the same reason I'm enjoying Gundam:IBO even though I never cared that much about giant mechas, but well-handled storytelling that explores and develops its cast is something I love seeing in shows. That's the reason why I often praise series such as Monogatari, Kokoro Connect, Moryou no Hako, Cowboy Bebop, Paranoia Agent, Space Brothers, Shirobako, Baccano, Higurashi and Non Non Biyori (as well as Humanity Has Declined as an outlier), and why I was really happy to find Say "I love you" thanks to this thread.
Then again, that doesn't mean I can't bring myself to enjoy "simpler" shows such as JoJo, KLK, Nozaki-kun or even To Love Ru, but I often feel I've got to be in a particular mood in order to actually enjoy them. Oddly enough, the same happens to me with Mushi-shi, which I just can't bring myself to enjoy at times despite regarding it highly.
I guess I'm fine with any genre as long as it's well-done and doesn't give me too many mixed signals of what it wants to do with its plot and characters. Having recently branched into romance with this show and mecha shows with IBO, I'd really like to get more recommendations for stuff I might be missing out on simply due to how I tend to overlook particular genres, with sports shows as a prime example.