A dark and unhandsome Heathcliff who seeks revenge and is a tortured soul.

Sir Laurence Olivier, Heathcliff in the classic 1939 William Wilder film
A "Gypsy" Heathcliff and wildly romantic. Only 1/2 the tale is told in this film. Along with Mr. Darcy, this role made Olivier's career in films

Ralph Fiennes in the 1992 film version of Wuthering Heights
A cross between a revengeful and romantic Heathcliff. This version presents the complete novel.

Timothy Dalton in 1970 Wuthering Heights - a more gentle retelling of the tale.
Watch him in a clip at Cathy's grave.
There are more Heathcliff actors (see link below). Even the singer Cliff Richards played him. But the above actors are the most well-known. Which is your favorite?
The Character of Heathcliff: The Reader's Guide to Wuthering Heights.