Self-esteem is important for so many reasons.
First, it's important for your own continued mental health. Thinking well of yourself is a need, not a want. Having suffered through depression for many years (and still struggling with it today), I know from experience the detrimental effects having a low self-image can have on your life as a whole. When you think well about yourself, you take better care of yourself, you maintain that image of wellness. And being around people who feel good about who they are makes other people feel good, too.
Second, self-esteem is generally more attractive than low self-esteem. This is important in attracting new partners to your relationships, but it's also important in the maintenance of your current relationships. Everyone wants to be with someone they find attractive, and a poor self-image can damage a person's attractiveness in very unpleasant ways. Moreover, it's contagious. When one person in a room feels down about themselves, it brings the people around them down, too. This can be a real strain on continuing to like someone.
Third, and I think maybe the most important, if you feel good about yourself, you're inclined to give the best of yourself to your partners. They get to see you at your pinnacle. And I know that, for me at least, when I see my girlfriends at their best, it makes me indescribably proud to be with them, to be a part of their lives. I can only hope the same is true for them. ^_^