Well generally only the artwork from manga inspire me. I, however, usually take note of commonly used themes, and the storytelling techniques manga use...that makes manga interesting. I'll just put some sort of image in my head, it may or not be inspired by any manga I've read, and I just start typing away. Well just recently I've kind of been a bit inspired by the movie "World of the Apes" to create a jungle-themed manga, haven't really gotten any work on that yet done though :P.
It also depends on the type of story as well. For something post-apocalyptic(something I'd done recently), I had the current world affairs as inspiration. And then there's the subject of similar themes in manga, but different portrayal. It's alright to take ideas and themes from other stories, but it's important to add your own originality, creativity, and style to the story. For example...you don't want people to easily be able to tell "This story feels too much like Naruto or Bleach." If i wanted to take the concept of "death gods" from Bleach or Death Note i'd make it so that there wasn't any organization in their society, that they were actually the antagonists, and that angels were trying to hunt them down...something like that :P... And if I were to use the concept of "ninjas" from Naruto, I'd make it so that the society was lead by a bunch of corporate baddies and the ninjas would settle with a corporation and go steal intel from other corporations. Of course that means the drawings of the ninjas will also have to be different. More dark clothings, more seinen(mature-like) and stealth-emphasized, and of course they wouldn't wear their corporation name on a headband like if they were from Naruto....