Lol, she's supposed to be a distant and closed off woman, with a sense of arrogance and abit of a domineering attitude due to certain things. Being adopted and raised by the Valentine nobles, she would have that haughty attitude and since she knows Cervy Beard is her father, she's a malfested, and her adopted dad lost it and died for his research of SE, she is quite distant. She also adopted a Machiavellian attitude by killing everyone (and I mean everyone) that is infected with Soul Edge's taint (SC2).
She's an incredibly strong woman though. Knowing she's malfested, she took a vow of chastity so her powers won't infect another victim. And despite all that she's been through, she never wavered and she has always pushed onward. When Cervy Beard devoured half her soul, she kept on going by fusing herself with a manufactured soul and defeated him in SCIV. Even her SC4 ending was quite impressive, as she's willing to die to end SE. Combined with the fact she's a talented and intelligent alchemist, Ivy isn't quite as dull as you think =3
*In fact, I can't really think of any char that has a dull personality. Maybe Mitsu and Amy though.
But you were talking about who's the most popular char in your previous post, not who's most important.
And as much as I love my little wind priestess, I can't say she's important as she had no effect at all on the storyline. Her importance may stem from her purifying abilities and from the fact she's one of the few characters that has the goal of saving the entire world since she loves everything about it, both good and bad. It's not perfect but she accepts and treasures it for what it's worth (unlike cough-Raph-cough new world yeaaaaa). But so far, she's not important. As evidenced by her removal (>T_T)
For important characters, the ones who wield the soul swords are the most important ones. After all, the game is all about them, so their wielders are the most important characters. Other chars are important if they contribute to the story, such as Ivy who helped awaken SC powers for Patty Cakes, or Zwei, who chose him to be the sword's wielder and killed Nighty.