Okay, this came from the wiki:
"Charming and with a very accommodating personality, Elisabeth was considered by many historians and contemporaries to be one of the most beautiful women in Europe at that time. As a young woman, she caught the eye of her elder cousin, the future German Emperor William II. He was a student then at Bonn University, and on weekends he often visited his Aunt Alice and his Hessian relatives. During these frequent visits, he became infatuated with Elisabeth, writing numerous love poems and regularly sending them to her. Flattered as she may have been by his attentions, Elisabeth was not attracted to William. She politely declined him, and the resulting heartbreak caused him to give up his studies and return to Prussia.
Besides William II, she had many other admirers, among them Lord Charles Montagu, the second son of the 7th Duke of Manchester, and Henry Wilson, later a distinguished soldier.
Yet another of Elisabeth's suitors was the future Frederick II, Grand Duke of Baden, William's first cousin. Queen Victoria described him as 'so good and steady", with "such a safe and happy position,' that when Elisabeth declined to marry him the Queen 'deeply regretted it'. Frederick's grandmother, the Empress Augusta, was so furious at Elisabeth's rejection of Frederick that it took some time for her to forgive Elisabeth."
Also, if she doesn't marry Sergei, Alexandra and Nicholas probably wouldn't meet and hemophilia wouldn't occur in the Imperial family.