I guess this is supposed to be the prompt that gets modern moviegoers to admit they like some really old movie. So, fine, here is the absolute oldest movie that I love and adore: The Sheik (1921).
I mentioned here how, as a teen, I developed a disdain for Rudolph Valentino, then later fell head over heels for him once I actually saw him in a movie. That movie was The Sheik. It's the movie that rocketed him to megastardom, making him the first true matinee idol. And if you watch it, it's not hard to see why. He's mysterious, handsome, and ruthless, but also tender. Not to mention, he looks great on a horse!
The plot? It's the stuff fluffy, romantic daydreams are made of :-) Headstrong, independent Lady Diana Mayo (Agnes Ayres) gets captured by Sheik Ahmed ben Hassan (Rudolph Valentino), who imprisons her in his lavish tent in the middle of nowhere, refusing to let her leave until she has, er, submitted to him. Of course, she refuses -- she hates him, she loathes him, she despises him...
And then she gets captured by a reeeeeeally horrible rival of Ahmed's. He's not going to do any of this waiting around nonsense like Ahmed. Of course, by this point Ahmed and Diana are in loooove, though they won't admit it. So Ahmed rescues Diana, though he gets bonked on the head in the process.
But all's well that ends well :-)
I just realized that I am now the same age Rudy was when he died: 31. Oh dear. Poor Rudy.
You can watch The Sheik here for free, and supposedly it's not chopped into segments like it would be on YouTube. It's part of something called The Video Cellar Collection, oodles of old movies and TV show episodes that are now in the public domain -- go here for a list of what they have.