Every good story has conflict. The trick is how you utilize it. Conflict can help your character grow, can give her something to overcome, can peak the reader's interest in the plot. If your character always gets everything she wants without having to fight for it, that can make for a really short, or a really boring story.
Conflict adds intrigue, creating tension in the narrative. It comes in many shapes and forms, both internal and external.
(wo)man vs. (wo)man - Harry vs. Voldemort; Ulysses vs. Medusa; Hector vs. Achilles... in each of these instances the villain is (eventually) corporeal, someone that must be defeated to ensure the hero's survival. The odds are stacked against the hero and he will have to use all his wits to gain the skills necessary to overcome his foe.
(wo)man vs. nature - Katniss vs. the Hunger Games arena... technically this is woman vs. a machine taking the form of nature, but you get the point. Fire and rain, lack of water and food, tracker-jackers, mockingjays, and muttations, all these "natural" forces test Katniss's skills and ability to survive, and teach her about herself (and the reader about her).
(wo)man vs. self - Ista vs. herself (Paladin of Souls, by Lois McMaster Bujold... love her, btw)... In this lovely novel Ista has to learn to move past the trauma she has experienced and allow herself to be open to using her gifts for the good of other characters in the story. The external conflicts here are secondary to the internal conflict, and her character grows and changes in beautiful ways by "The End."
Knowing your character's back story can help you discern when conflict will come up (ex: Hermione's muggle-born status fuels her desire to excel; Sirius and Snape's past animosity causes clashes when they are forced to work on the same side; Snape's love for Lily Potter motivates him to agree to protect her son, but his hatred for James Potter makes him antagonize Harry at every opportunity). The best conflict has a reason, even if it never has a resolution. Snape never forgave Harry for being James' son and it's hard to tell if Harry ever forgave Snape for killing Dumbledore... but the poignancy of the emotions that the conflict between those two characters creates is one of the most memorable aspects of that series.
So what conflicts arise in the lives of your characters (major OR minor)?