I second Nana, and third A place farther than the universe!! lol
I love Fruits Basket to death. I cried so many times reading the manga, and I'm so happy they finally did a proper anime adaption.
(you need an account to see links)
It's about a high school girl named Tohru Honda, who finds herself living with the mysterious Sohma family after her mother passes away. The Sohmas are cursed such that when they are hugged by someone of the opposite sex, they turn into one of the animals of the Chinese Zodiac. Tohru promises to keep their secret and, as she becomes more involved with the family, she learns about their individual struggles and helps them come to terms with their curse. This series is known for its strong character development and emotional themes, but it also has a lot of comedy and drama.
I also really like Miss Kobayashi's Dragon Maid! It's super funny, cute, and fluffy.
(you need an account to see links)
Miss Kobayashi's Dragon Maid is about a young programmer named Kobayashi who saves the life of a dragon named Tohru and as a result, Tohru decides to repay the favor by becoming her maid. But Tohru isn’t the only dragon to have found her way to the human world and soon, a group of dragons show up at Kobayashi's door, each with their own personalities and quirks. This show is a comedic slice of life with fantasy elements, featuring the daily lives of these dragons as they try to adapt to life in the human world.
Both MC's named Tohru, hopefully not confusing, lol.