What makes older movies look "old"?

Well, you need the costumes to look old.

Yes you're on the right track. You would need an analog camera, meaning it would use film. Frame rates are usually the key to giving video footage its "look." Television shows and movies look different because movies generally are filmed at a lower frame rate (23-25 frames a second) while television is at nearly 30 frames a second. This gives TV a "live" feel, while the lower frame rates in movies make scenes solid and limits what I'd call excessive motion effects. There are many differences between digital and analog, but yeah just using a good quality analog movie camera would give that old look.

well... if you going to want to make a movie look years before. you will need to work with your costumes,props,storyline, dialouge, and lighting. I dont think the camera matters its all in the hands of the editor to work with the feeling and the cinematographer. There are some editing plugins where u just drop it into the film and it makes it look like an old movie. but you cant add plugin to make it look like in the 60s and have a prop or costume that didnt exist back then. unless you doing it for the fun and not to be perfect

Because old movies become a classic that shows how they make improve to get better filming that before first films were very short with black and white. But from on, all films are getting better that have longer movie with color and more actors and actresses.