As I started thinking more about this, a lot of my avoided-films are because of the stars involved, or a genre.
Elizabeth Taylor leaves me cold. I don't think I've ever seen any of her films for more than a scene or two. And if Richard Burton's in it (HOT TIN ROOF, CLEO, etc), I won't even stay that long.
Charlie Chaplin. Not a fan. I love Keaton, but don't care for Chaplin, although I've seen most of GOLD RUSH, CITY LIGHTS and MODERN TIMES. That was the extent of my patience. But Laurel & Hardy? Sure. Harold Lloyd? Oh yes. Buster Keaton? Any day of the week. I think my anti-Chaplin stance comes from some perception of "meanness", although L&H, Lloyd and Keaton also had similar unpleasantries written for them.
I avoided most musicals (even the 'modern' GREASE), although SINGIN' IN THE RAIN and MY FAIR LADY have somehow slipped into my Favorites list.