In the late 90s, Heath Ledger arrived in Hollywood after a successful TV career in his home country, Australia. He was on the hunt for work and was looking for his big break when he decided to audition for the role of Max Evans on what was shaping up to be the hottest new sci-fi show on the planet, Roswell. The Fox Network was looking for a strong male actor to carry the show and the be main love interest for the show's central female character, Liz Parker.
Side Note: Yes, Roswell was initially supposed to be a Fox show... but they ended up passing on it and it was transferred over to the WB network.
At this stage, Ledger had not yet starred in '10 Things I Hate About You', which is widely considered to be his breakout role. Before that movie was released at the end of 1999, he was still considered to be pretty green amongst acting folk and the big wig Executives were just not impressed with what he had to offer.
Prior to this audition, Ledger had starred in a short-lived Fox show called 'Roar'. The show was about an Irish man who united a bunch of Celtic clans in order to fight off the invading Romans. It was a massive flop, both commercially and critically. It was crucified by critics and universally hated by audiences (except for a handful of die hard fans). It represented a massive stain on Ledger's career.
After the epic failure of Roar, Ledger's agent fought hard and secured him an audition for Roswell and, rumour has it, he tested strongly for the role. However, history was not on Ledger's side on this fateful day. Fox Executives remembered Ledger from Roar and they feared audiences would as well. They did not want to taint Roswell and take a risk, especially since Roswell had such an enormous budget behind it.
Ultimately, the Producers at Fox passed on Ledger and decided to go with Jason Behr. They had seen Behr on 7th Heaven and Dawson's Creek, and believed he had what it takes to portray a mysterious and brooding teenage alien. They were right.
As it turns out, the rejection was a blessing in disguise. With a free schedule, he was able to fly back to Australia and film the dark comedy 'Two Hands'. It received critical acclaim and landed Ledger an AFI nomination for 'Best Performance by an Actor in a Leading Role'. Despite not winning the award, the nomination gave him the credibility he needed to really make an impact on Hollywood. As soon as his work on Two Hands was completed, he flew back to Hollywood and landed himself the leading role in '10 Things I Hate About You', which instantly catapulted him to teen heartthrob status.
It's interesting how things panned out. If Ledger had been cast as 'Max Evans', he would not have filmed the movies that kick started his career... and possibly, wouldn't have ended up playing The Joker... and could even still be alive today.