Here are some films I would endorse for the any gamer-to-be to watch.
The single criterion here is how inspirational these films would be, to inspire a would-be-gamer to actively get into gaming.
Films mentioned (and some additional films) in my top 50 picks (must see films) in alphabetical order
Blazing Saddles
Braveheart
Cinderella (animated)
The Chronicles of Narnia (animated)
Conan the Barbarian
Fantasia (animated)
Forbidden Planet
Heavy Metal (animated)
King Kong (original)
King Kong (remake by Peter Jackson)
Mary Poppins
The Matrix
The Neverending Story
The Pink Panther
Peter Pan (any version, including the film Hook)
Pirates of the Caribbean
The Princess Bride
Raiders of the Lost Ark
Snow White and the Seven Dwarves (animated)
Spartacus
The Terminator
The Thing (original only)
The Three Musketeers (Gene Kelly)
Time Bandits
The Wizard of Oz
Films mentioned (and some additional films) I'd rank somewhere between 51 and 100 (very heavily recommended) in alphabetical order
Alien
Army of Darkness
Bambi (animated)
Bedknobs and Broomsticks
The Blob (original)
Bram Stoker's Dracula (any version)
Fantasia 2000 (animated)
Excalibur
Gladiator
Indiana Jones and the Last Crusade
Indiana Jones and the Temple of Doom
James Bond (most of these films)
Jane Eyre (original and remake)
Jason and the Argonaunts
Ladyhawke
Man of La Mancha
Monty Python and the Holy Grail
Night of the Living Dead
The Odyssey
The Rocky Horror Picture Show
Robin Hood (Errol Flynn and most other versions, including Robin Hood - Prince of Thieves)
The Secret Garden
Dr Seuss (most of the animated films)
Sherlock Holmes (many of these films)
Sinbad and the Seven Seas
The Legend of Sleepy Hollow (animated)
Terminator II: Judgement Day
Weird Science
Films mentioned I'd rank somewhere between 101 and 150 (highly recommended) in alphabetical order
Aliens
An American Werewolf in Paris
King Arthur
Batman (the first film)
City Slickers and City Slickers 2 - The Legend of Curly's Gold
Crouching Tiger, Hidden Dragon
Day of the Triffids
Dragonslayer
Dune
Edward Scissorhands
Elizabeth (Cate Blanchett)
Flatliners
The Good, the Bad, and the Ugly
Highlander
Interview with the Vampire
Joan of Arc (Lili Sobieski)
Labyrinth
The Land that Time Forgot
The Lawnmower Man
Lawrence of Arabia
Mad Max
The Man in the Iron Mask
Monty Python's Life of Brian
Predator
Santa Claus (animated, Frank Baum's story)
Spaceballs
Terminator III: Rise of the Machines
War of the Worlds (original)
Films mentioned I'd rank somewhere between 151 and 200 (recommended) in alphabetical order
Anthony and Cleopatra
Apocalypse Now
The Beastmaster
Clash of the Titans
Dawn of the Dead
Eric the Viking
Masque of the Red Death
Monty Python's History of the World Part 1
Pinnochio (animated)
The Quick and the Dead
The Road Warrior
Tarzan (animated)
Troy
Van Helsing
Weathering Continent (animated)
Willow
Films mentioned I'd rank 201+ (not crucial: watch when you can) in alphabetical order
Aliens 3 and 4
Batman (all others after the first)
Buffy the Vampire Slayer (film, the series is better)
Big Trouble in Little China
Conan the Destroyer
The Craft
The Dark Crystal
Dawn of the Dead (remake)
Day of the Dead
Earthsea (Sci-Fi miniseries) *I'd HIGHLY recommend the books, however*
Legend
Quills
Red Sonja
The Scorpion King
Sleepy Hollow (the live action film)
Superman (all)
Tarzan (older version)
Films mentioned I can't rank, because I do not remember them well enough or haven't seen them (in alphabetical order also)
13th Warrior, Arabian Nights, The Mists of Avalon, Baron Mancheusen, Ben Hur, The Big Sleep, Bulletproof Monk, Blade 1, Brotherhood of the Wolf, The Cell, The Cinderella Story, Constantine, The Count of Monte Cristo, The Covenant, The Chronicles of Narnia, The Crow, Cutthroat Island, Dagon, Dark Kingdom, Dragon Inn, Dungeons and Dragons 1 (and 2), Escaflowne, Fairytale, Fire and Ice (Animated), First Knight, Flight of the Dragons, The Gnomemobile, The Golden Child, The Goonies, Gunga Din, Hawk the Slayer, Hercules, Hero, House of Flying Daggers, Howl's Moving Castle, Immortals, The Island at the Top of the World, Isle of Dr. Moreau, Kaena the Prophesy, Kingdom of Heaven, A Knight's Tale, Krull, Krull the Conqueror, Laputa, Lara Croft - Tomb Raider, The Librarian, The Long Ships, The Magical Legend of the Leprechauns, Mirrormask, Merlin, Princess Mononoke, In the Mouth of Madness, The Mummy, The Mummy Returns, Musa the Warrior, The Mysterious Island, The Name of the Rose, National Treasure, Nausicaa of the Valley of the Wind, Pirates of the Caribbean (sequel), Reign of Fire, Roar, Robin Hood: Men in Tights, Seven Samurai, Shang-re-La, Shaun of the Dead, Shipwrecked, Snowwhite, Spirited Away, Timeline, The Treasure of the Sierra Madre, Treasure Island, Tristan & Isolde (2005), Underworld, The Last Unicorn (animated), V for Vendetta, Prince Valiant (1997), What Dreams May Come