Here's my list of Great Johnny Depp Movies. Some may disagree, since Depp now has so many movies from his career, but in my opinion these are the best Johnny Depp movies:

Edward Scissorhands
The movie that really launched Depp's career. The message is clear and wonderfully inventive, a great parable about the alienation of the different and misunderstood.

What's Eating Gilbert Grape
Great movie about caring for misfits and fun to see Leonardo DiCaprio before he became the bee's knees. One of the best Johnny Depp movies.

Donnie Brasco
This movie just exemplifies the coolness of Depp. He definitely did not have as many lines as Al Pacino who was talking constantly, but had a strong presence.

Fear and Loathing in Las Vegas
The critics did not love this movie but it is so strange and wonderfully visual it became an instant cult classic. If it turns into a cult classic it has to go on the list

Blow
One of those ultra cool movies where maybe the acting is not terrific, but such a fun story to follow. The critics did not love this one either, but got great reviews from the audience.

Pirates of the Caribbean - The Curse of the Black Pearl
The first Pirates movie and I think the best, they should have either stopped making these after this one or spend a little more time to make them better.

Charlie and the Chocolate Factory
I love Johnny Depp in this movie. just a super strange character and Depp seems the perfect person to play it. In many ways it is better than the original. Director Tim Burton adds his usual signature strangeness to the film.

Sweeney Todd: The Demon Barber of Fleet Street
One of the only musicals I have ever liked, and that is saying a lot.