Filled in, verified or corrected the rest...in BOLD. A (?) means I'm not 100% certain:
R1: Airplane, Top Gun, Psycho, The Addams Family, Let There Be Blood, Titanic (co-production w/ 20th Century Fox), Transformers
R2: The Godfather, Friday the 13th, Jackass: The Movie, Wayne's World, Paranormal Activity, Crocodile Dundee, The Hunt for Red October
R3: Catch 22, Nashville, ST: TMP, Rosemary's Baby, Raiders of the Lost Ark, Beverly Hills Cop, Cleopatra
R4: 48 HRS, Murder On the Orient Express, Spongebob: The Movie, Zoolander, Ferris Bueller, Planes Trains & Automobiles, Ghost (not Indiana Jones & The Last Crusade, which was 1989, not 1990)
R5: Cheech & Chong's Up in Smoke, Bad News Bears, Scrooged(?), Mission Impossible, Breakfast at Tiffany's, Forrest Gump, Cloverfield
R6: True Grit, Escape From Alcatraz, The Truman Show, The Warriors, The Naked Gun
R7: Team America: World Police, Paper Moon, Willy Wonka, Pretty in Pink, No Country for Old Men
R8: Duck Soup, Vertigo, An Inconvenient Truth, Jekyl & Hyde, Trading Places, An Officer and a Gentleman, Rango
R9: Curious Case Of Benjamin Button, Barbarella, Days of Thunder, The Nutty Professor, Indiana Jones & The Temple of Doom, Harold and Maude (not Easy Rider), Fatal Attraction
R10: Coming to America, Mommie Dearest, GI: Joe, Chariots of Fire, Serpico, Beavis and Butthead Do America, Footloose
R11: Tomb Raider, King Kong, Gulliver's Travels, Double Indemnity, Queen Elizabeth (w/Sarah Bernhardt), War of the Worlds, Dreamgirls
R12: School of Rock, Sunset Boulevard, Flashdance, The Godfather Part II, Super 8, Chinatown, The Fighter
R13: Tintin, Justin Bieber: Never Say Never(?), Pet Cemetery, The Longest Yard, Sullivan's Travels*, Rear Window, The Italian Job
*Technically, Sullivan's Travels was released in 1941, but it came out so close to the end of that year that most Paramount theaters didn't get it until 1942