Elizabeth and Darcy meet several times. Which are their most important meetings?

Certainly, one of the most important meetings between Elizabeth and Darcy is their first one because it inaugurates her prejudice toward him, a prejudice that will remain in place for much of the novel.  Within her hearing, Bingley encourages Darcy to dance with Elizabeth, and Darcy replies, 

"She is tolerable; but not handsome enough to tempt me; and I am in no humour at present to give consequence to young ladies who are slighted by other men.  You had better return to your partner and enjoy her smiles, for you are wasting your time with me."

His rudeness is atrocious, and the fact that he caught her eye just prior to insulting her seems to confirm that he doesn't care if she hears him.  When she later related the story at home, she did so "with much bitterness of spirit and some exaggeration [of] the shocking rudeness of Mr. Darcy."  From this meeting onward, Elizabeth only finds fodder for her dislike of the man.  He can do no right.

That is, until he proposes to her.  This interaction, and the letter Darcy writes to Elizabeth immediately after, is another key one.  His proposal only confirms her belief in his terrible pride, for though he "spoke of apprehension and anxiety, [...] his countenance expressed real security."  Despite his insults to her family and references to her "inferiority," he seems assured of his success, and this infuriates her.  In her rejection, she accuses him of both separating Bingley from Jane and of behaving dishonorably to Wickham.  In his letter, delivered to her the following day, he addresses both charges, and -- as angry as she is -- Elizabeth is forced to acknowledge that Darcy actually behaved honorably in both situations, especially given his lack of familiarity with Jane's character.  This causes her to reevaluate herself, and especially her own vanity in thinking she is such a good judge of character.  She says, 

"Pleased with the preference of one, and offended by the neglect of the other, on the very beginning of our acquaintance, I have courted prepossession and ignorance, and driven reason away, where either were concerned.  Till this moment, I never knew myself."

Realizing that her prejudice against Mr. Darcy, formed at their first meeting, has clouded her judgment ever since, Elizabeth resolves change going forward, for "In her own past behaviour, there was a constant source of vexation and regret [...]."

The last crucial meeting occurs at his home, Pemberley.  She visits the house with her aunt and uncle, believing the family to be away.  However, she bumps into Darcy, and their mutual embarrassment seems to betray that there has been no alteration in his feelings for her and a great alteration in her feelings for him.  She thought, 

That he should even speak to her was amazing! -- but to speak with such civility, to enquire after her family!  Never in her life had she seen his manners so little dignified, never had he spoken with such gentleness as on this unexpected meeting.

Later, when Darcy visits Elizabeth in Lambton, introducing her to his sister, the Gardiners appear to be in little doubt as to her feelings and no doubt as to his.  After this meeting, it does not take long for Elizabeth to realize that "he was exactly the man, who, in disposition and talents, would most suit her."

The book is called Pride and Prejudice, after all, so the meeting that initiates Elizabeth's prejudice against Darcy as a result of his pride, the letter that removes her prejudice, and the subsequent meeting that shows him without pride, seem to be the most important to our understanding of their relationship.