I think part of the reason I like anime and manga so much is that it often inspires me, and that does of course lead to things I make being largely influenced by anime and manga.
Thing is, I don't know if it's really the graphical style that does it. Oh, I mean, there are aspects of the style that are significant--large eyes make expressing emotions easier, for example--but mostly it just seems to be that they have standardized a few things that Western animation and comics still haven't, and that makes for stuff that is much more exciting for a maker.
For example, animation-wise, continuity, a (relatively) short ongoing plot that gets wrapped up in the end and character development are fairly common. That's not to say it's always well done, but it's there, and that's not as often true with American cartoons....which is fairly limiting for a person interested in the art form. There are some western shows that do that (and they inspire me pretty much equally. I'm thinking of shows like Gargoyles and more recently, Avatar. Although since that one's so heavily influenced by anime, that might not be a great example).
Manga-wise, continuity and character development are pretty standard, but at least in the mainstream stuff, a fixed length plot isn't. Mainstream stuff tends to be ongoing. It's also largely superheroes. Indie stuff has changed that a bit, but indie stuff is harder to find (I still can't find a copy of Scott Pilgrim at any of my local stores, for instance), and there have always been limited series.
Anyway, these are just some thoughts off the top of my head. I'll probably have some more to say later.