Here's the list I made for a couple of friends who just joined Netflix, unfortunately I couldn't put Raise The Red Lantern or Dellamorte Dellamore (Cemetery Man) on it since there aren't region 1 DVDs yet.
(movie descriptions simplified for my semi-ignorant friends

)
Hong Kong - martial arts
- Iron Monkey (be sure to get the 1993 PG-13 disc, they have an older version)
- A Chinese Ghost Story - good mix of martial arts and sorcery
- The Bride With White Hair - more swords and sorcery
- The Heroic Trio - super-heroines vs. super-villains (avoid the awful dub track!)
Hong Kong - "gun operas": crime dramas with exaggerated, operatic battles.
- The Killer (John Woo directed, he went on to do Face/Off and Mission Impossible 2)
- Hard-Boiled - John Woo's other great HK film
- A Better Tomorrow - not as quite as good, but some memorable scenes
- Time and Tide: Special Edition (2000) - an amazing extended sequence in a tenement
(just endure the bad HK comedy at the start)
French - "gun operas" directed by Luc Besson (The Fifth Element)
- La Femme Nikita - inspired the TV series and bad Bridget Fonda US remake
- Leon: The Professional - classic, set in the US so no subtitles needed
- Wasabi - a comedy of a Frenchman in Japan, written but not directed by Besson
French ? more serious fare
- The Big Blue / Le Grand Bleu - very interesting story of competitive free-divers
- Le Dernier Combat - almost-silent, black-and-white, post-apocalyptic tale
- Krzysztof Kieslowski's amazing "Three Colors" trilogy of loosely connected films:
1. Blue / Bleu
2. White / Blanc
3. Red / Rouge
- Brotherhood of the Wolf - OK it's actually a period piece martial-arts werewolf murder-mystery, but it's good!
German
- Das Boot - you've probably seen it, but if not an excellent WW2 drama
- Run Lola Run - a clever punk variation on the Groundhog Day theme
Norway
Insomnia (1997) - original version of the movie about a detective trying to solve a murder while coping with 24-hour daylight
Taiwan
Eat Drink Man Woman - good drama about a master chef and his family
Japan - Comedy
Tampopo - comedy about (among other things) the search for the perfect ramen recipe
Japan - Samurai
- Ran - lush epic of the battle for succession between sons of a warlord
- Chushingura - slow, good drama of the story told to DeNiro in Ronin about masterless samurai avenging their lord.
- Seven Samurai - film that inspired The Magnificent Seven
- Yojimbo - film that inspired Clint Eastwood's Fistful of Dollars
- Zatoichi - series of films about a blind master swordsman
Japanese - Animation (anime) (best watched with subtitles!)
- Ghost in the Shell - SciFi story, one of the inspirations for The Matrix
- Hayao Miyazaki's films, he's an icon of Japanese animation, with the same stature that Walt Disney had in his prime:
1. Spirited Away - reminds me of a Brothers Grim or Hans Christian Anderson tale
2. Princess Mononoke - action / heroic fantasy
3. Kiki's Delivery Service - sweet story about a little girl witch growing up
4. Castle In The Sky - the most Disney-like, but inventive and original
- Spriggan - what if Jet Li or Steven Seagal replaced Harrison Ford in Raiders of the Lost Ark?
- Cowboy Bebop - good SF action series about far-future bounty hunters
- Lain - this series is a weird cross between x-files, twin peaks, and cyberpunk
- Noir - female assassins with mysterious pasts, the anime La Femme Nikita / Leon
- RahXephon - stylish series about alien invaders and giant robots