Dramas
Perfect Match - after a cosmetical treatment her face is ugly and she feel insecure... that is when she meets him... (she is not insecure in general)
Second Love - she is a chem teacher and don't like her life or herself. Than a young, strange dancer confess his love to her...
Kurosaki Kun No Iinari Ni Nante Naranai and
Black Davil and White Prince (actually one series) - she is transfaired to a new school and she wants everything to change, because she know she is too insecure and too shy. Than she meets two guys: the black davil and the white prince.
Movie
Kimi Ni Todoke - the most famous boy of the school fall in love with a quiet, insecure girl, that get bullied by others (don't know the movie but I loved the Anime)