Johnny Depp reportedly turned down Jack over the script; Jared Leto was reportedly favored but would not audition, and the actress transcribed as Claire Daines was supposedly wanted for Rose. — Bill Simmons
Jeremy Sisto auditioned multiple times and is lamented as never finding the right part; Billy Crudup was considered but was committed to Without Limits. — Bill Simmons
Robert De Niro was reportedly offered Captain Smith but declined due to a gastrointestinal infection; he would have been fun in the role. — Bill Simmons
Kate Winslet had to do a screen test, watchable online, opposite Jeremy Sisto, Elton from Clueless, who auditioned but probably was not in contention; the major name in contention for Jack Dawson was Matthew McConaughey.
Stephen Dorff is the verified one: a New York Daily News piece headlined 'actor is thankful he didn't get Titanic role' has the Blade co-star saying he wanted a career like Johnny Depp, Sean Penn and Jack Nicholson and an Oscar, which Titanic would have made impossible, and that Leo will always be the guy on the boat.
One host disagrees that Leo is the guy on the boat, since he has been in so many hits and everyone has a favorite Leo, whereas Matt Damon and Ben Affleck are more locked into their 90s work; Sofia Coppola is said to have made Somewhere with Dorff because he never blew up, and Titanic will be in the first line of DiCaprio's obituary, and of Billy Zane's.
Billy Zane has not done much anyone has heard of since, though he has been in three times as many films as Kate Winslet.
Chris O'Donnell, named on Wikipedia for Jack, would have been a great and adorable Jack given his Batman movies and a season-two television arc, but could not have taken the film past a billion dollars; Leo is singular and the chemistry is enduring, though he seems strikingly innocent and little in it.
Rob Lowe was in the mix for Cal and is a great asshole, as in St. Elmo's Fire; pre-West Wing he might not have pulled viewers out of the film, though one host says he would have a little, and the leads mostly had blank or clean reputations at the time, which the hosts think mattered.