Hello,

I'm looking for any mangas with a submissive girl that is crazily in love with the protagonist. She is willing to do absolutely anything for him/her but sees herself as inferior to others.

I'd be especially grateful if it's yuri/shoujo-ai but normal manga is OK too. No yaoi please.

Deep Love - Ayu no Monogatari is the first that comes to mind. It fits your description exactly (without the yuri) but it has mature themes and is definitely a story that'll make you cry. She is devoid of hope in the beginning and thinks of her own life as worthless. Her views changes as the story goes on. Especially when she meets a certain male main character.

Midori no Hibi is in the male protagonist point of view and is very funny. The girl is attached to his hand and is willing to do anything for him because she loves him. However, I'm not sure if she sees herself as inferior to others.

Midnight Secretary female protagonist isn't exactly totally submissive (she definitely doesn't see herself as inferior to other). Yet still she's willing to anything for the male main character because of first a sense of duty to her job then for love to male main character.

Koharu no Hibi