1. Her sass.
Ziva has been through a lot in her life. Her father trained her to be a Mossad agent from a very young age, and there have been many events in her life that have deeply wounded her. Life has never been easy for Ziva, and she may try to hide her scars, but she keeps going and eventually learns to heal.
3. Her friendships with the other characters.
During Ziva's time on the show, she became close to many characters, especially Abby and Gibbs. The friendship that became most important to her, however, was her friendship with Tony. Even though there was always some heat and tension between them, their friendship was always the most important part of their complicated relationship, and that was built on mutual trust and respect.
4. Her unintentional funniness.
5. Her fighting skills.
If anyone thinks that women can't fight as well as men can, I will point you to two examples. The first is Black Widow. The second is Ziva David. Ziva's kick-ass combat skills have gotten the NCIS team out of many sticky situations, and it's impressive to watch.
6. Her intelligence and investigation skills.
Ziva is extremely talented. Not only is she good at fighting, but she's also good at figuring things out and taking initiative. She's highly-trained and has a good head on her shoulders to figure out what to do next. She's good at generating theories in an effort to figure out what's going on. Ziva became an important part of Gibbs' team, and her contributions to NCIS--both the show and the organization--are numerous.
Reasons 1, 2, and 3 by Amanda.
Reasons 4, 5, and 6 by Sky.