What Nonlethal Force said. Much anime and "modern" fantasy contains aesthetics and ideas that I don't care for.
That said, I don't have the knee-jerk reaction some people do. That is, if I see something I don't like, I don't like it no matter where it's from. If I see something I like, I don't care if it comes from anime, WoW, or some other source.
It's just that, more often than not, there's more overlap in my personal taste with the older fantasy tropes than the newer ones.