He always wanted to direct a James Bond movie, but Albert R. Broccoli rejected him twice. The first time, early in his career, Broccoli turned him down because he was young, inexperienced, and unknown. He approached Broccoli again after directing Jaws, but Broccoli wouldn't hire him because he was afraid he'd demand too much money.
He was going to have a small cameo in Casper that was actually filmed, but later cut for pacing.
Interstellar was written for him to direct. Many have noted that a certain plot twist near the end would fit far better into a Spielberg film than a Christopher Nolan one.
He has always expressed an intention to direct a musical. He once noted that 1941 was planned as one but changed during its chaotic production. Later he was attached to a project about opera divas but that was shelved. The closest he came was the opening of Indiana Jones and the Temple of Doom.
His dream may come true, however. As evidenced here, he is very eager to do an adaptation of West Side Story.