What roles do you think

He would have become an A-lister after The Dark Knight. I think he would have won the Oscar even if he hadn't died

Probably he would have worked with Christopher Nolan again. He might have gotten the role that went to Joseph Gordon-Levitt in Inception

And he would've probably been in demand by many of the top directors

He was only 28 when he died, it's pretty crazy to think about that. Most actors haven't even entered their prime at that age. De Niro, Pacino, and Nicholson received their first Oscar nominations in their 30s

So yeah, the world would have been his oyster. He could have gotten pretty much any role he'd want

I know this will sound very silly, but back in the days, something like one year before Heath Ledger died, I had read The Deerslayer written by James Fenimore Cooper (the author of Last of the Mohicans as well). In that novel, there is a character called Henry March, and with all the descriptions that were given, I pictured Heath Ledger and no one else in the role. I was even thinking: "If I ever had to become a movie director and adapt this book, Heath Ledger is the only actor for THAT part.

One year after reading the novel, he died. So... now I just don't see anyone playing that particular part lol.