I'd recommend:
- Glass Mask
- Hime-chan's Ribbon
- Kimi ni Todoke
- Lovely Complex
- Mujin Wakusei Survive
All fantastic shows, and with no violence at all. Most of these are shoujo, and very light-hearted. If you're looking to laugh, I highly recommend Lovely Complex. If you're looking for more of a drama, watch Glass Mask.